RTIF连接参考-07-8-7
07.秋季-八年级-第7讲-垂直平分线与角平分线 教师版
第八讲 垂直平分线与角平分线 姓名：______【知识导航】【知识要点】一、 垂直平分线线段垂直平分线：经过线段中点并且垂直在这条线段的直线.线段垂直平分线性质定理：垂直平分线上的点与这条线段两个端点的距离相等. 简记：“垂分线 斜线段相等”.线段垂直平分线判定定理（逆定理）：与一条线段两个端点距离相等的点，在这条线段的垂直平分线上. 简记：“斜线段相等 垂分线”. 【例题详解】 【例 1】 如图，在△ABC 中，已知BC 比AC 长3cm ，AB 的垂直平分线交BC 于点D ，交AB 于点E ，△ACD的周长是15cm ，求BC 和AC 的长．【解析】∵DE 是AB 的垂直平分线，∴AD=BD ，∴△ACD 的周长=AC+AD+CD=AC+BD+CD=AC+BC ，由题意得，315BC AC AC BC −=⎧⎨+=⎩，解得96BC AC =⎧⎨=⎩．∴BC 和AC 的长分别为9cm ，6cm ．【例 2】 如图，在R t △ABC 中，∠ACB =90°，∠A =22.5°，斜边AB 的垂直平分线交AC 于点D ，点F 在AC 上，点E 在BC 的延长线上，CE =CF ，连接BF ，DE ．线段DE 和BF 在数量和位置上有什么关系？并说明理由．【解析】DE =BF ，DE ⊥BF ．理由如下：连接BD ，延长BF 交DE 于点G ． ∵点D 在线段AB 的垂直平分线上， ∴AD =BD ，∴∠ABD =∠A =22.5°．在R t △ABC 中，∵∠ACB =90°，∠A =22.5°， ∴∠ABC =67.5°，∴∠CBD =∠ABC ﹣∠ABD =45°， ∴△BCD 为等腰直角三角形，垂直平分线与角平分线垂直平分线角平分线∴BC =DC ．在△ECD 和△FCB 中， CE CF DCF BCF CD CB =⎧⎪∠=∠⎨⎪=⎩， ∴R t △ECD ≌R t △FCB （SAS ）， ∴DE =BF ，∠CED =∠CFB ． ∵∠CFB +∠CBF =90°， ∴∠CED +∠CBF =90°， ∴∠EGB =90°，即DE ⊥BF ．【例 3】 如图，在△ABC 中，AB 边垂直平分线交BC 于点D ，AC 边垂直平分线交BC 于点E ，连接AD 、AE ．（1）若∠BAC=110°，求∠DAE 的度数； （2）若∠BAC=θ（0°＜θ＜180°），求∠DAE 的度数（用含θ的式子表示）【解析】（1）∵AB 的垂直平分线交BC 于点D ，AC 的垂直平分线交BC 于点E ， ∴DB=DA ，EC=EA ， ∵∠BAC =110°， ∴∠B+∠C=70°， ∵DB=DA ，EC=EA ，∴∠DAB=∠B ，∠EAC =∠C ， ∴∠DAB+∠EAC =70°，∴∠DAE=110°﹣70°=40°， （2）分两种情况：①如图所示，当∠BAC ≥90°时， ∵DM 垂直平分AB ， ∴DA=DB ， ∴∠B=∠BAD ，同理可得，∠C=∠CAE ，∴∠BAD+∠CAE =∠B+∠C=180°﹣θ，∴∠DAE=∠BAC ﹣（∠BAD+∠CAE ）=θ﹣（180°﹣θ）=2θ﹣180°；②如图所示，当∠BAC ＜90°时， ∵DM 垂直平分AB ， ∴DA=DB ， ∴∠B=∠BAD ，同理可得，∠C=∠CAE ，∴∠BAD+∠CAE =∠B+∠C =180°﹣θ，∴∠DAE=∠BAD+∠CAE ﹣∠BAC =180°﹣θ﹣θ=180°﹣2θ．【例 4】 如图所示，在ABC Rt ∆中，︒=∠90ACB ，BC AC =，D 为BC 边上的中点，AD CE ⊥于点E ，AC BF ∥交CE 的延长线于点F ，求证：AB 垂直平分DF ．【解析】连接DF ，90BCE ACE ∠+∠=︒，90ACE CAE ∠+∠=︒， BCE CAE ∴∠=∠．AC BC ⊥，//BF AC ．BF BC ∴⊥．90ACD CBF ∴∠=∠=︒， AC CB =，ACD CBF ∴∆≅∆．CD BF ∴=．12CD BD BC ==，BF BD ∴=．BFD ∴∆为等腰直角三角形．90ACB ∠=︒，CA CB =，45ABC ∴∠=︒．90FBD ∠=︒，45ABF ∴∠=︒．ABC ABF ∴∠=∠，即BA 是FBD ∠的平分线．BA ∴是FD 边上的高线，BA 又是边FD 的中线， 即AB 垂直平分DF ．二、 角平分线1．一般地，从一个角的顶点出发，把这个角分成两个相等的角的射线，叫做这个角的平分线．2．角平分线的性质定理：角平分线上的点到角的两边的距离相等．3．角平分线的判定定理：在角的内部，到角的两边的距离相等的点在角平分线上． 【例题详解】【例 5】 已知，如图AB=AC ，∠A =108°，BD 平分∠ABC 交AC 于D ，求证：BC=AB+CD ．【解析】证明：在线段BC 上截取BE=BA ，连接DE ．∵BD 平分∠ABC ，∴∠ABD =∠EBD =12∠ABC ． 在△ABD 和△EBD 中，BE BA ABD EBD BD BD =⎧⎪∠=∠⎨⎪=⎩，∴△ABD ≌△EBD ．（SAS ） ∴∠BED=∠A =108°，∠ADB=∠EDB ． 又∵AB=AC ，∠A=108°，∠ACB =∠ABC=12×（180°﹣108°）=36°， ∴∠ABD=∠EBD =18°．∴∠ADB =∠EDB =180°﹣18°﹣108°=54°． ∴∠CDE =180°﹣∠ADB ﹣∠EDB =180°﹣54°﹣54°=72°． ∴∠DEC =180°﹣∠DEB =180°﹣108°=72°． ∴∠CDE=∠DEC ． ∴CD=CE ．∴BC=BE+EC=AB+CD ．【例 6】 在▱ABCD 的两边AD ，CD 上各取一点F ，E ，连接AE ，CF 交于点P ，且AE =CF ．求证：PB 平分∠APC ．【解析】证明：连接BE ，BF ，过B 作BN ⊥CF ，BM ⊥AE ，∵四边形ABCD 是平行四边形，∴S △ABE =S △BFC =12S 平行四边形ABCD ，∴12•AE ×BM =12CF •BN ， ∵AE =CF ，∴BM =BN ， ∴PB 平分∠APC ．【例 7】 如图，在△ABC 中，∠ABC 的平分线与∠ACB 的外角的平分线相交于点P ，连接AP ．（1）求证：P A 平分∠BAC 的外角∠CAM ；（2）过点C 作CE ⊥AP ，E 是垂足，并延长CE 交BM 于点D ．求证：CE =ED ．【解析】证明：（1）过P 作PT ⊥BC 于T ，PS ⊥AC 于S ，PQ ⊥BA 于Q ，如图，∵在△ABC 中，∠ABC 的平分线与∠ACB 的外角的平分线相交于点P ， ∴PQ =PT ，PS =PT ， ∴PQ =PS ，∴AP 平分∠DAC ，即P A 平分∠BAC 的外角∠CAM ；（2）∵P A 平分∠BAC 的外角∠CAM ， ∴∠DAE =∠CAE ， ∵CE ⊥AP ，∴∠AED =∠AEC =90°， 在△AED 和△AEC 中 DAE CAE AE AEDEA CEA ∠=∠⎧⎪=⎨⎪∠=∠⎩∴△AED ≌△AEC ， ∴CE =ED ．【例 8】 如图，△ABC 中，∠A =60°，∠ACB 的平分线CD 和∠ABC 的平分线BE 交于点G ．求证：GE=GD ．【解析】连接AG ，过点G 作GM ⊥AB 于M ，GN ⊥AC 于N ，GF ⊥BC 于F ．∵∠A =60°，∴∠ACB+∠ABC =120°， ∵CD ，BE 是角平分线， ∴∠BCG+∠CBG=120°÷2=60°， ∴∠CGB =∠EGD =120°，∵G 是∠ACB 平分线上一点， ∴GN=GF ，同理，GF=GM ， ∴GN=GM ，∴AG 是∠CAB 的平分线， ∴∠GAM=∠GAN =30°，∴∠NGM=∠NGA+∠AGM =60°+60°=120°， ∴∠EGD =∠NGM =120°， ∴∠EGN =∠DGM ， 又∵GN=GM ，∴Rt △EGN ≌Rt △DGM （AAS ）， ∴GE=GD ．三、 综合练习【例 9】 如图，OE ，OF 分别是△ABC 中AB ，AC 边的中垂线（即垂直平分线），∠OBC 、∠OCB 的平分线相交于点I ，试判定OI 与BC 的位置关系，并给出证明．【解析】OI ⊥BC ．理由：连接OA ，过点I 作IM ⊥OB 于点M ，过点I 作IN ⊥OC 于点N ，过点I 作IG ⊥BC 于点G ， ∵OE ，OF 分别是AB ，AC 边的中垂线， ∴OA =OB ，OA =OC ， ∴OB =OC ，∵∠OBC ，∠OCB 的平分线相交于点I ， ∴IM =IG ，IN =IG ， ∴IM =IN ，∴点I 在∠BOC 的角平分线上， ∴OI ⊥BC ．【例 10】 如图，ABC ∆中，AD 平分BAC ∠，DG BC ⊥且平分BC ，DE AB ⊥于E ，DF AC ⊥于F ．（1）说明BE CF =的理由；（2）如果5AB =，3AC =，求AE 、BE 的长．【解析】（1）证明：连接BD ，CD ，AD 平分BAC ∠，DE AB ⊥，DF AC ⊥， DE DF ∴=，90BED CFD ∠=∠=︒， DG BC ⊥且平分BC ， BD CD ∴=，在Rt BED ∆与Rt CFD ∆中， BD CDDE DF =⎧⎨=⎩， Rt BED Rt CFD(HL)∴∆≅∆， BE CF ∴=；（2）在AED ∆和AFD ∆中， 90AED AFD EAD FADAD AD ∠=∠=︒⎧⎪∠=∠⎨⎪=⎩， ()AED AFD AAS ∴∆≅∆， AE AF ∴=，设BE x =，则CF x =，5AB =，3AC =，AE AB BE =−，AF AC CF =+， 53x x ∴−=+， 解得：1x =，1BE ∴=，514AE AB BE =−=−=．【备用题】【例 11】 已知如图，梯形ABCD 中，AD ∥BC ，以两腰AB ，CD 为一边分别向两边作正方形ABGE 和DCHF ，设线段AD 的垂直平分线l 交线段EF 于点M ，EP ⊥l 于P ，FQ ⊥l 于Q ． 求证：EP=FQ ．【解析】过D 作PN 的平行线分别交FQ 、BC 于点K 、L ，设AD 的垂直平分线交AD 于N ，在△FKD 与△DLC 中，∠DFK =90°﹣∠FD K=∠CDL ，∠FKD =∠DLC =90°，DF=DC ， ∴△FKD ≌△DLC ， ∴FK=DL ，∴FQ=FK+KQ=DL+DN ， 同理可得，EP=DL+AN ， 又∵MN 为AD 中垂线，∴AN=ND，∴EP=FQ【巩固练习】 1. 如图，在ABC ∆中，AC AB =，︒=∠120A ，cm BC 12=，AB 的垂直平分线交BC 于点M ，交AB于点E ，AC 的垂直平分线交BC 于点N ，交AC 于点F ，则MN 的长为 ．【解析】∵AB=AC ，∴∠B=∠C ，∵∠A=120°，∴∠B=∠C=30°， 连接AM ，AN ，∵ME 是AB 的垂直平分线，∴AM=BM ，∠BAM=∠B=30°，∴∠CAM=∠BAC ﹣∠BAM=120°-30°=90°， ∴CM=2AM=2BM ， ∴3BM=BC=12cm ，∵BM=4cm ，同理可得，CN=4，∴MN=BC ﹣CN ﹣BM=12﹣4﹣4=4（cm ）．2. 如图，在△ABC 中，BD 是∠ABC 的平分线，EF 垂直平分BD ．求证：∠ABD =∠BDF ．【解析】∵EF 垂直平分BD ，∴FB=FD ，∴∠FBD =∠BDF ，∵BD 是∠ABC 的平分线， ∴∠ABD=∠FBD ， ∴∠ABD =∠BDF ．3. 如图，已知∠AOB =40°，点P 关于OA 、OB 的对称点分别为C 、D ，CD 交OA 、OB 于M 、N 两点，求∠MPN 的度数是多少？ 【解析】∠OMN=x, ∠ONM=y .得∠PMN =180°-2x , ∠PNM =180°-2y , ∠MPN=2x+2y-180°. 由x+y+40°=180°,得∠MPN=100°．4.如图，四边形ABCD中，∠B=90°，AB∥CD，M为BC边上的一点，且AM平分∠BAD，DM平分∠ADC．求证：（1）AM⊥DM；（2）M为BC的中点．【解析】（1）∵AB∥CD，∴∠BAD+∠ADC=180°，∵AM平分∠BAD，DM平分∠ADC，∴2∠MAD+2∠ADM=180°，∴∠MAD+∠ADM=90°，∴∠AMD=90°，即AM⊥DM；（2）作NM⊥AD交AD于N，∵∠B=90°，AB∥CD，∴BM⊥AB，CM⊥CD，∵AM平分∠BAD，DM平分∠ADC，∴BM=MN，MN=CM，∴BM=CM，即M为BC的中点．5.如图，在△ABC中，DM、EN分别垂直平分AC和BC，交AB于M、N，（1）若△CMN的周长为21cm，求AB的长；（2）若∠MCN=50°，求∠ACB的度数．【解析】（1）∵DM、EN分别垂直平分AC和BC，∴AM=CM，CN=BN，∵△CMN的周长为18cm，即CM+CN+MN=18，∴AM+BN+MN=AB=18cm．∴AB=18cm．（2）∵DM垂直平分AC，∴∠1=∠2，∵EN垂直平分BC，∴∠3=∠4，又∵∠1+∠2+∠3+∠4+50°=180°，则2（∠1+∠4）=180°﹣50°=130°，∠1+∠4=65°，∴∠ACB=（∠1+∠4）+∠MCN=65°+50°=115°．6.已知△ABC的两条角平分线BD，CE交于点O，OD=OE，∠ABC=70°，求∠A的度数．【解析】∴∠ABC+∠ACB=180°﹣∠A，∵△ABC的两条角平分线BD、CE交于O，∴∠OBC=12∠ABC，∠OCB=12∠ACB，∴∠BOC=180°﹣（∠OBC+∠OCB）=180°﹣12（∠ABC +∠ACB ）=180°﹣12（180°﹣∠A ）=90°+12∠A ，∴∠EOD =90°+12∠A ，连接OA ，作OF ⊥AB 于点F ，OG ⊥AC 于点G ，OH ⊥BC 于点H ，∵△ABC 的两条角平分线BD 、CE 交于O ， ∴OF =OG =OH ，在R t △EOF 和R t △DOG 中，OF OGOE OD =⎧⎨=⎩∴R t △EOF ≌R t △DOG （HL ）， ∴∠EOF =∠DOG ， ∴∠FOG =∠EOD ， ∵OF ⊥AB ，OG ⊥AC ， ∴∠A +∠FOG =180°， ∴∠A +∠EOD =180°， ∴∠A +90°+12∠A =180°，∴∠A =60°． 如图，过点O 作FO ⊥AC 于F ，OG ⊥AB 于G ， ∴OG =OF同上的方法得，R t △OGE ≌R t △OFD ， ∴∠EOG =∠DOF ， ∵∠BOE =∠COD ， ∴∠BOG =∠COF ，∵OG =OF ，∠BGO =∠CFO ， ∴△BOG ≌△COF ， ∴∠ABO =∠ACE ，∵BD ，CE 是△ABC 的角平分线， ∴∠ACB =∠ABC =70°， ∴∠A =180°﹣70°﹣70°=40° 故答案为60°或40°。
无线网桥组网设置详细说明
54M 无线网桥UBNT 固件桥接设置说明建议非专业用户请使用我们得快速配置文件自动配置参数，简单快捷注意：如对此款设备不熟悉或者不需要其她设置得，非本文中介绍得其她参数保持默认就好，不要随便做更改，请 先仔细阅读此说明后再操作以免减少不必要得麻烦网桥通过POE 电源接线到电脑，更改电脑本地连接IP 地址为指定192、168、1、50,设备得接线方式以及更改本 地连接步骤参照《步骤一设备接线方式》。
【登陆后台设置页面】打开上网浏览器，进入192、168、1、20管理页面，用户名密码均为ubnt ，如果浏览器输入地址后页面一片空白， 右键点击页面空白处选择--编码--选择UTF-8,或者更换其她浏览器测试。
INTERFACE LANGUAGE下面开始介绍简单得两个网桥做桥接，一个设置成发射端、一个设置成接收端 【设置发射端】 第一步：进入“NETWORK ”选项页面 下图-网络模式：选择网桥（注：里边有高级路由模式，不明白此应用得不要随便选择此模式） -Disable Network ：保持默认None ，此选项就是禁用端口，不要做任何更改否则设备无法进入后台。
-网桥IP 地址：注意不要选择DHCP ，选项静态，然后设置IP 地址我们就是设置默认得192、168、1、20 （注意： 设置桥接得时候发射端跟接收端得IP 要分开，不要重复，比如这个发射端我们设置得就是192、168、1、20，那接 收端得设备IP 就设置成192、168、1、21，如果一个局域网内有多个网桥设备得话那每一个网桥都设置一个不同得 IP 不要重复，如果就是做监控得话注意网桥得IP 地址也不要跟摄像头得IP 重复了，在每一个页面更改参数后都要 点击最下面得“更改”按钮，在点击页面上方提示得“应用”，否则不生效。
Language:LOGO CUSTOMIZATIONEnable Custom Logo:Lego Target URL:EnglishEr^lish Cesk?Frarcsi^ Polski Pod:ugue = Espanol 中交£简体xSet as default【页面中文切换】进入后台默认英文，改为中文页面，如下图找到SYSTEM 选项页面，下面找到Language 语言选项，选择简体中第二步：进入“亚也£1£55”设置页面下图- 网络模式：选择接入点或者接入点WDS （注：“站”为接收模式，“接入点”为发射模式）- SSID ：设备发射得wifi 信号名称，可自己随便填写，在这我们设置得就是ubnt001，不能设置中文。
RT12864-0
/*--------------------------------------------------------------*///Note: RT12864J-1液晶显示//CS1(左)-CS2(右), 是高电平有效!!!//该液晶是行扫描!!!//每8位显示数据是低位在上, 高位在下//测试硬件//单片机: c8051f020//模式://晶振: 24MHz//#include<intrins.h>#include "c8051F020.h"#define uchar unsigned char#define uint unsigned intuint i,j;/*--------------------------------------------------------------*///系统时钟#define SYSCLK 24000000/*--------------------------------------------------------------*///字库码的引索/*(0) !(1) "(2) #(3) $(4) %(5) &(6) '(7)((8) )(9) *(10) +(11) ,(12) -(13) .(14) /(15)0(16) 1(17) 2(18) 3(19) 4(20) 5(21) 6(22) 7(23)8(24) 9(25) :(26) ;(27) <(28) =(29) >(30) ?(31)@(32) A(33) B(34) C(35) D(36) E(37) F(38) G(39)H(40) I(41) J(42) K(43) L(44) M(45) N(46) O(47)P(48) Q(49) R(50) S(51) T(52) U(53) V(54) W(55)X(56) Y(57) Z(58) [(59) \(60) ](61) ^(62) _(63)`(64) a(65) b(66) c(67) d(68) e(69) f(70) g(71)h(72) i(73) j(74) k(75) l(76) m(77) n(78) o(79)p(80) q(81) r(82) s(83) t(84) u(85) v(86) w(87)x(88) y(89) z(90) {(91) |(92) }(93) ~(94)*//*--------------------------------------------------------------*//*--------------------------------------------------------------*/// 字体: LCD1602字体//取码规则: 低位在前, 列行扫描, 阴码(1-亮, 0-灭)//查表方法: 要显示的ASCII码-32就可以得到字库码的指针unsigned char code Font_code[][5] = {{0x00,0x00,0x00,0x00,0x00},// (0){0x00,0x00,0x4F,0x00,0x00},//!(1){0x00,0x07,0x00,0x07,0x00},//"(2){0x14,0x7F,0x14,0x7F,0x14},//#(3){0x24,0x2A,0x7F,0x2A,0x12},//$(4){0x36,0x49,0x55,0x22,0x50},//&(6) {0x00,0x05,0x03,0x00,0x00},//'(7) {0x00,0x1C,0x22,0x41,0x00},//((8) {0x00,0x41,0x22,0x1C,0x00},//)(9) {0x14,0x08,0x3E,0x08,0x14},//*(10) {0x08,0x08,0x3E,0x08,0x08},//+(11) {0x00,0x50,0x30,0x00,0x00},//,(12) {0x08,0x08,0x08,0x08,0x08},//-(13) {0x00,0x60,0x60,0x00,0x00},//.(14) {0x20,0x10,0x08,0x04,0x02},///(15) {0x3E,0x51,0x49,0x45,0x3E},//0(16) {0x00,0x42,0x7F,0x40,0x00},//1(17) {0x42,0x61,0x51,0x49,0x46},//2(18) {0x21,0x41,0x45,0x4B,0x31},//3(19) {0x18,0x14,0x12,0x7F,0x10},//4(20) {0x27,0x45,0x45,0x45,0x39},//5(21) {0x3C,0x4A,0x49,0x49,0x30},//6(22) {0x01,0x71,0x09,0x05,0x03},//7(23) {0x36,0x49,0x49,0x49,0x36},//8(24) {0x06,0x49,0x49,0x29,0x1E},//9(25) {0x00,0x36,0x36,0x00,0x00},//:(26) {0x00,0x56,0x36,0x00,0x00},//;(27) {0x08,0x14,0x22,0x41,0x00},//<(28) {0x14,0x14,0x14,0x14,0x14},//=(29) {0x00,0x41,0x22,0x14,0x08},//>(30) {0x02,0x01,0x51,0x09,0x06},//?(31) {0x32,0x49,0x79,0x41,0x3E},//@(32) {0x7E,0x11,0x11,0x11,0x7E},//A(33) {0x7F,0x49,0x49,0x49,0x3E},//B(34) {0x3E,0x41,0x41,0x41,0x22},//C(35) {0x7F,0x41,0x41,0x22,0x1C},//D(36) {0x7F,0x49,0x49,0x49,0x41},//E(37) {0x7F,0x09,0x09,0x09,0x01},//F(38) {0x3E,0x41,0x49,0x49,0x7A},//G(39) {0x7F,0x08,0x08,0x08,0x7F},//H(40) {0x00,0x41,0x7F,0x41,0x00},//I(41) {0x20,0x40,0x41,0x3F,0x01},//J(42) {0x7F,0x08,0x14,0x22,0x41},//K(43) {0x7F,0x40,0x40,0x40,0x40},//L(44) {0x7F,0x02,0x04,0x02,0x7F},//M(45) {0x7F,0x04,0x08,0x10,0x7F},//N(46) {0x3E,0x41,0x41,0x41,0x3E},//O(47) {0x7F,0x09,0x09,0x09,0x06},//P(48){0x7F,0x09,0x19,0x29,0x46},//R(50) {0x46,0x49,0x49,0x49,0x31},//S(51) {0x01,0x01,0x7F,0x01,0x01},//T(52) {0x3F,0x40,0x40,0x40,0x3F},//U(53) {0x1F,0x20,0x40,0x20,0x1F},//V(54) {0x3F,0x40,0x38,0x40,0x3F},//W(55) {0x63,0x14,0x08,0x14,0x63},//X(56) {0x03,0x04,0x78,0x04,0x03},//Y(57) {0x61,0x51,0x49,0x45,0x43},//Z(58) {0x00,0x7F,0x41,0x41,0x00},//[(59) {0x15,0x16,0x7C,0x16,0x15},//\(60) {0x00,0x41,0x41,0x7F,0x00},//](61) {0x04,0x02,0x01,0x02,0x04},//^(62) {0x40,0x40,0x40,0x40,0x40},//_(63) {0x00,0x01,0x02,0x04,0x00},//`(64) {0x20,0x54,0x54,0x54,0x78},//a(65) {0x7F,0x48,0x44,0x44,0x38},//b(66) {0x38,0x44,0x44,0x44,0x20},//c(67) {0x38,0x44,0x44,0x48,0x7F},//d(68) {0x38,0x54,0x54,0x54,0x18},//e(69) {0x08,0x7E,0x09,0x01,0x02},//f(70) {0x0C,0x52,0x52,0x52,0x3E},//g(71) {0x7F,0x08,0x04,0x04,0x78},//h(72) {0x00,0x44,0x7D,0x40,0x00},//i(73) {0x20,0x40,0x44,0x3D,0x00},//j(74) {0x7F,0x10,0x28,0x44,0x00},//k(75) {0x00,0x41,0x7F,0x40,0x00},//l(76) {0x7E,0x02,0x0C,0x02,0x7C},//m(77) {0x7E,0x04,0x02,0x02,0x7C},//n(78) {0x38,0x44,0x44,0x44,0x38},//o(79) {0x7C,0x14,0x14,0x14,0x08},//p(80) {0x08,0x14,0x14,0x18,0x7C},//q(81) {0x7C,0x08,0x04,0x04,0x08},//r(82) {0x48,0x54,0x54,0x54,0x20},//s(83) {0x04,0x3F,0x44,0x40,0x20},//t(84) {0x3C,0x40,0x40,0x20,0x7C},//u(85) {0x1C,0x20,0x40,0x20,0x1C},//v(86) {0x3C,0x40,0x30,0x40,0x3C},//w(87) {0x44,0x28,0x10,0x28,0x44},//x(88) {0x0C,0x50,0x50,0x50,0x3C},//y(89) {0x44,0x64,0x54,0x4C,0x44},//z(90) {0x00,0x08,0x36,0x41,0x00},//{(91) {0x00,0x00,0x7F,0x00,0x00},//|(92){0x08,0x04,0x08,0x10,0x08},//~(94){0x08,0x08,0x2A,0x1C,0x08},//→(127){0x08,0x1C,0x2A,0x08,0x08},//←(128){0x04,0x02,0x7F,0x02,0x04},//↑(129){0x10,0x20,0x7F,0x20,0x10}};//↓(130)/*--------------------------------------------------------------*///指令宏定义#define Display_On 0x3f //显示开指令#define Display_Off 0x3e //显示关指令#define Y_Col_Addr 0x40 //定位到第0列指令(列起始地址)(0-63)#define X_Page_Addr 0xb8 //定位到第0页指令(页起始地址)(0-7)#define Start_Line 0xc0 //定位从DDROM中的第0行开始往屏幕上显示/*--------------------------------------------------------------*///便于理解宏定义//清屏参数#define LSCR 0 //左屏#define RSCR 1 //右屏#define ASCR 2 //全屏/*--------------------------------------------------------------*///数据接口定义sbit RS = P3^0; //数据指令控制端//高电平数据，低电平指令sbit RW = P3^1; //读写控制端//高电平写入，低电平读出sbit E = P3^2; //使能端//下降沿写入数据，高电平读出sbit CS1 = P3^3; //左边屏幕使能//高电平有效sbit CS2 = P3^4; //右边屏幕使能//高电平有效sbit RST = P3^5; //LCD复位端//低电平复位#define Data_IO P4 //数据传输端口/*--------------------------------------------------------------*///选屏宏定义#define LCD_sel_left {CS2 = 0; CS1 = 1;}#define LCD_sel_right {CS2 = 1; CS1 = 0;}#define LCD_sel_all {CS2 = 1; CS1 = 1;}/*--------------------------------------------------------------*/#define Hard_RST {RST = 0; RST = 1;} //硬件复位/*--------------------------------------------------------------*///函数声明(私有)void Delay(uint ms){for(i=0;i<ms;i++)for(j=0;j<300;j++);}/*--------------------------------------------------------------*/ //读出指令(状态)uchar LCD_read_cmd(void){uchar read_cmd;Data_IO = 0xff; //输入RW = 1; //读出RS = 0; //指令E = 1; //高电平读出read_cmd = Data_IO; //指令return (read_cmd);}/*--------------------------------------------------------------*/ //读出数据//先只须空读一次, 以后接着就无须空读//空读之后读出的数据都是有效的!!!uchar LCD_read_dat(void){uchar read_dat;Data_IO = 0xff; //输入RS = 1; //数据RW = 1; //读出E = 1; //高电平读出read_dat = Data_IO; //数据return (read_dat);}/*--------------------------------------------------------------*/ //检查忙标志位void LCD_check_busy(void){uchar lcd_status;do{lcd_status=LCD_read_cmd();}while(lcd_status & 0x80);}/*--------------------------------------------------------------*/ //写入指令void LCD_write_cmd(uchar cmd){LCD_check_busy();RW = 0; //写入RS = 0; //指令Data_IO = cmd; //指令E = 1;Delay(1);E = 0; //下降沿写入}/*--------------------------------------------------------------*/ //写入数据void LCD_write_dat(uchar dat){LCD_check_busy();RW = 0; //写入RS = 1; //数据Data_IO = dat; //数据E = 1;Delay(1);E = 0; //下降沿写入}/*--------------------------------------------------------------*/ //显示清屏void LCD_clr_scr(uchar sel_dat){uchar i, j;if(sel_dat == 0) LCD_sel_leftelse if(sel_dat == 1) LCD_sel_rightelse if(sel_dat == 2) LCD_sel_allLCD_write_cmd(Y_Col_Addr);LCD_write_cmd(X_Page_Addr);for(j = 0; j < 8; j++){LCD_write_cmd(X_Page_Addr + j);for(i = 0; i < 64; i++) LCD_write_dat(0x00);}}/*--------------------------------------------------------------*/ //液晶字节定位(8*1)//液晶规划://x: 0 - 7 (行)//y: 0 -127 (列)void LCD_byte_pos(uchar x, uchar y){if(y < 64) LCD_sel_left //左半屏else {y -= 64; LCD_sel_right} //右半屏LCD_write_cmd(X_Page_Addr + x); //页地址0-7LCD_write_cmd(Y_Col_Addr + y); //列地址0-63}/*--------------------------------------------------------------*///液晶字符输出(8*5字体)//x: 0 - 7 (行)//y: 0 -25 (列)void LCD_print(uchar x, uchar y, uchar c_dat){uchar i;y = y * 5;if(y<125)for(i = 0; i < 5; i++){LCD_byte_pos(x,y+i);LCD_write_dat(Font_code[c_dat - 32][i]);}}/*--------------------------------------------------------------*///液晶字符串输出//x: 0 - 7 (行)//y: 0 -25 (列)void LCD_prints(uchar x, uchar y, uchar *s_dat){while(*s_dat) {LCD_print(x, y++, *s_dat++);}}/*--------------------------------------------------------------*///初始化LCD128*64//清除所有显示DDRAM, 清除画面内容, 所有地址指针回0 void LCD_init_12864(void){Hard_RSTLCD_clr_scr(ASCR); //清全屏LCD_write_cmd(Display_Off); //关闭显示LCD_write_cmd(X_Page_Addr); //起始页地址LCD_write_cmd(Start_Line); //起始行LCD_write_cmd(Y_Col_Addr); //起始列地址LCD_write_cmd(Display_On); //开启显示}/*--------------------------------------------------------------*///显示Run模式void Disp_Run(){LCD_prints(0, 0, "Run Modes:");LCD_prints(1, 2, "Charge&AutoRun");LCD_prints(2, 2, "Remote Control");LCD_prints(3, 2, "Demo Auto-Run");LCD_prints(4, 2, "Self-Test");}/*--------------------------------------------------------------*/void SYSCLK_Init(void){int n;OSCXCN = 0x67; // EXTERNAL Oscillator Control Registerfor (n = 0; n < 255; n++) ; // wait for osc to startwhile ( (OSCXCN & 0x80) == 0 ); // wait for xtal to stabilize OSCICN = 0x88; // Internal Oscillator Control Register}/*--------------------------------------------------------------*/void PORT_Init(void){XBR2=0x40;P3MDOUT = 0x3F;P74OUT =0x03;}/*--------------------------------------------------------------*///主函数void main(void){WDTCN=0xDE;WDTCN=0xAD; //关看门狗SYSCLK_Init();PORT_Init();LCD_init_12864();do{LCD_prints(1, 2, "Charge&AutoRun");Delay(10000);}while(1);}/*--------------------------------------------------------------*/。
专题01 全等三角形(解析版)
2021-2022学年人教版数学八年级上册压轴题专题精选汇编专题01 全等三角形一．选择题1．（2020秋•东城区期末）如图所示，点O是△ABC内一点，BO平分∠ABC，OD⊥BC于点D，连接OA，若OD＝5，AB＝20，则△AOB的面积是（ ）A．20B．30C．50D．100【思路引导】根据角平分线的性质求出OE，最后用三角形的面积公式即可解答．【完整解答】解：过O作OE⊥AB于点E，∵BO平分∠ABC，OD⊥BC于点D，∴OE＝OD＝5，∴△AOB的面积＝，故选：C．2．（2020秋•定西期末）如图，在四边形ABCD中，∠A＝90°，AD＝4，连接BD，BD⊥CD，∠ADB＝∠C．若P是BC边上一动点，则DP长的最小值为（ ）A．4B．3C．2D．1【思路引导】根据垂线段最短得出当DP⊥BC时，DP的长最小，求出∠ABD＝∠CBD，根据角平分线的性质得出此时DP＝AD，再得出选项即可．【完整解答】解：当DP⊥BC时，DP的长最小，∵BD⊥CD，∴∠BDC＝90°，∵∠A＝90°，∠ADB＝∠C，∠A+∠ADB+∠ABD＝180°，∠BDC+∠C+∠CBD＝180°，∴∠ABD＝∠CBD，∵∠A＝90°，∴当DP⊥BC时，DP＝AD，∵AD＝4，∴DP的最小值是4，故选：A．3．（2020秋•莫旗期末）如图，AB∥CD，BE和CE分别平分∠ABC和∠BCD，AD过点E，且与AB互相垂直，点P为线段BC上一动点，连接PE．若AD＝8，则PE的最小值为（ ）A．8B．5C．4D．2【思路引导】过E作EP⊥BC于P，此时PE的值最小，求出AD⊥CD，根据角平分线的性质求出AE＝DE＝PE，求出AE的长即可．【完整解答】解：过E作EP⊥BC于P，此时PE的值最小，∵AB∥CD，AD⊥AB，∴AD⊥CD，∵BE和CE分别平分∠ABC和∠BCD，∴AE＝PE，ED＝PE，∴AE＝ED＝PE，∵AD＝8，∴PE＝4，即PE的最小值是4，故选：C．4．（2020秋•鞍山期末）如图，Rt△ABC中，∠C＝90°，AD平分∠BAC交BC于点D，过点D作DF⊥AB，垂足为点F，点E在边AC上，若DE＝DB，则下列结论不正确的是（ ）A．DC＝DF B．DE＝BF C．AC＝AF D．AB＝AC+CE【思路引导】根据全等三角形的判定和性质解答即可．【完整解答】解：∵Rt△ABC中，∠C＝90°，AD平分∠BAC交BC于点D，过点D作DF⊥AB，垂足为点F，∴DC＝DF，故A正确，在Rt△DCE与Rt△DFB中，，∴Rt△DCE≌Rt△DFB（HL），∴CE＝BF，故B错误，在Rt△ADC与Rt△ADF中，，∴Rt△ADC≌Rt△ADF（HL），∴AC＝AF，故C正确，∴AB＝AF+BF＝AC+CE，故D正确，故选：B．5．（2020秋•新宾县期末）如图，AB＝AD，AC＝AE，∠DAB＝∠CAE＝50°，以下四个结论：①△ADC≌△ABE；②CD＝BE；③∠DOB＝50°；④点A在∠DOE的平分线上，其中结论正确的个数是（ ）A．1B．2C．3D．4【思路引导】证明△ADC≌△ABE（SAS），可得出CD＝BE，∠ADC＝∠ABE，则得出∠DOB＝50°，连接OA，过点A作AM⊥CD于点M，AN⊥BE于点N，证明△ABN≌△ADM（AAS），则可得出点A在∠DOE的平分线上．【完整解答】解：∵∠DAB＝∠CAE＝50°，∴∠DAB+∠BAC＝∠CAE+∠BAC，∴∠DAC＝∠BAE，在△ADC与△ABE中，，∴△ADC≌△ABE（SAS），∴CD＝BE；故①，②正确；如图1，若AB与CD相交于点F，∵△ABE≌△ADC，∴∠ADC＝∠ABE，∵∠AFD＝∠CFB，∴∠DOB＝∠DAB＝50°．故③正确．如图2，连接OA，过点A作AM⊥CD于点M，AN⊥BE于点N，∴∠AMD＝∠ANB＝90°，∵△ABE≌△ADC，∴∠ABN＝∠ADM，在△ABN和△ADM中，，∴△ABN≌△ADM（AAS），∴AN＝AM，∴点A在∠DOE的平分线上．故④正确．故选：D．6．（2020秋•金昌期末）如图，AD是△ABC的角平分线，CE⊥AD，垂足为F．若∠CAB＝30°，∠B＝55°，则∠BDE的度数为（ ）A．35°B．40°C．45°D．50°【思路引导】根据三角形的内角和求出∠ACB＝95°，利用三角形全等，求出DC＝DE，再利用外角求出答案．【完整解答】解：∵∠CAB＝30°，∠B＝55°，∴∠ACB＝180°﹣30°﹣55°＝95°，∵CE⊥AD，∴∠AFC＝∠AFE＝90°，∵AD是△ABC的角平分线，∴∠CAD＝∠EAD＝×30°＝15°，又∵AF＝AF，∴△ACF≌△AEF（ASA）∴AC＝AE，∵AD＝AD，∠CAD＝∠EAD，∴△ACD≌△AED（SAS），∴DC＝DE，∴∠DCE＝∠DEC，∵∠ACE＝90°﹣15°＝75°，∴∠DCE＝∠DEC＝∠ACB﹣∠ACE＝95°﹣75°＝20°，∴∠BDE＝∠DCE+∠DEC＝20°+20°＝40°，故选：B．7．（2020秋•宜兴市期中）如图，在△ABC中，AB＝4，∠ABC＝60°，∠ACB＝45°，D是BC的中点，直线l经过点D，AE⊥l，BF⊥l，垂足分别为E，F，则AE+BF的最大值为（ ）A．B．C．D．【思路引导】把要求的最大值的两条线段经过平移后形成一条线段，然后再根据垂线段最短来进行计算即可．【完整解答】解：如图，过点C作CK⊥l于点K，过点A作AH⊥BC于点H，在Rt△AHB中，∵∠ABC＝60°，AB＝4，∴BH＝2，AH＝2，在Rt△AHC中，∠ACB＝45°，∴AH＝CH＝2，∴AC＝＝＝2，∵点D为BC中点，∴BD＝CD，在△BFD与△CKD中，，∴△BFD≌△CKD（AAS），∴BF＝CK，延长AE，过点C作CN⊥AE于点N，得矩形ENCK，∴CK＝EN，∴AE+BF＝AE+CK＝AE+EN＝AN，在Rt△ACN中，AN＜AC，当直线l⊥AC时，最大值为2，综上所述，AE+BF的最大值为2．故选：B．8．（2020秋•江岸区校级月考）如图，方格中△ABC的三个顶点分别在正方形的顶点（格点上），这样的三角形叫格点三角形，图中可以画出与△ABC全等的格点三角形共有（ ）个．（不含△ABC）A．28B．29C．30D．31【思路引导】当点B在下面时，根据平移，对称，可得与△ABC全等的三角形有8个，包括△ABC，当点B在其它3条边上时，有3×8＝24（个）三角形与△ABC全等，由此即可判断．【完整解答】解：当点B在下面时，根据平移，对称，可得与△ABC全等的三角形有8个，包括△ABC，当点B在其它3条边上时，有3×8＝24（个）三角形与△ABC全等，∴一共有：8+24﹣1＝31（个）三角形与△ABC全等，故选：D．二．填空题9．（2020秋•南岗区校级月考）如图，在△ABC中，AD⊥BC，CE⊥AB，垂足分别为D、E，AD、CE交于点H，已知EH＝EB＝3，AE＝5，则CH的长为 2 ．【思路引导】先由AD⊥BC，CE⊥AB，判断出∠ADB＝∠AEH＝90°，再判断出∠BAD＝∠BCE，进而判断出△HEA≌△BEC，得出AE＝EC＝5，即可得出结论．【完整解答】解：∵AD⊥BC，CE⊥AB，∴∠ADB＝∠AEH＝90°，∵∠AHE＝∠CHD，∴∠BAD＝∠BCE，在△HEA和△BEC中，，∴△HEA≌△BEC（AAS），∴AE＝EC＝5，则CH＝EC﹣EH＝AE﹣EH＝5﹣3＝2．故答案为：2．10．（2020•松北区一模）在△ABC中，点D在AC上，AD＝5，AB+AC＝16，E是BD中点，∠ACB＝∠ABC+2∠BCE，则CD＝ 2 ．【思路引导】延长CE于F，使CE＝EF，交AB于点G，根据SAS证明△BEF与△DEC全等，进而利用全等三角形的性质解答即可．【完整解答】解：延长CE于F，使CE＝EF，交AB于点G，∵E是BD的中点，∴BE＝DE，在△BEF与△DEC中，，∴△BEF≌△DEC（SAS），∴∠F＝∠DCE，BF＝DC，∵∠ACB＝∠ABC+2∠BCE，∴∠DCE＝∠ACB﹣∠BCE＝∠ABC+∠BCE，∵∠AGC＝∠ABC+∠BCE，∴∠AGC＝∠DCE，∴∠F＝∠DCE＝∠AGC＝∠BGF，AG＝AC，∴BF＝BG＝CD，设BF＝BG＝CD＝x，∵AD＝5，AB+AC＝16，∴，解得：x＝2，∴CD＝2，故答案为：2．11．（2020•荷塘区模拟）在△ABC中，若其内部的点P满足∠APB＝∠BPC＝∠CPA＝120°，则称P为△ABC的费马点．如图所示，在△ABC中，已知∠BAC＝45°，设P为△ABC的费马点，且满足∠PBA＝45°，PA＝4，则△PAC的面积为 4 ．【思路引导】如图，延长BP交AC于D，先说明△ABD是等腰直角三角形，△ADP是30°的直角三角形，可得PD和AD的长，根据费马点的定义可得∠APC＝120°，从而可知△PDC也是30°的直角三角形，可得CD的长，根据三角形的面积公式可得结论．【完整解答】解：如图，延长BP交AC于D，∵∠BAC＝∠PBA＝45°，∴∠ADB＝90°，AD＝BD，∵P为△ABC的费马点，∴∠APB＝∠CPA＝120°，∴∠BAP＝180°﹣120°﹣45°＝15°，∴∠PAC＝45°﹣15°＝30°，∴∠APD＝60°，Rt△PAD中，∵PA＝4，∴PD＝2，AD＝2，∵∠APC＝120°，∴∠CPD＝120°﹣60°＝60°，Rt△PDC中，∠PCD＝30°，∴CD＝2，∴AC＝AD+CD＝2+2＝4，∴△PAC的面积为＝＝4．故答案为：4．12．（2020秋•海珠区校级期中）如图，AD是△ABC的角平分线，DF⊥AB，垂足为点F，DE＝DG，△ADG 和△ADE的面积分别为50和39，则△EDF的面积为 5.5 ．【思路引导】在线段AC上取一点M，使DM＝DE，过点D作DN⊥AC，利用角平分线的性质得到DN＝DF，将三角形EDF的面积转化为三角形DNM的面积来求．【完整解答】解：如图，在线段AC上取一点M，使DM＝DE，过点D作DN⊥AC于点N，∵DE＝DG，∴DM＝DG，∵AD是△ABC的角平分线，DF⊥AB，∴DF＝DN，在Rt△DEF和Rt△DMN中，，∴Rt△DEF≌Rt△DMN（HL），∵△ADG和△AED的面积分别为50和39，∴S△MDG ＝S△ADG﹣S△ADM＝50﹣39＝11，∴S△DNM ＝S△EDF＝S△MDG＝×11＝5.5．故答案是：5.5．13．（2020秋•青羊区校级月考）如图，在△ABC中，∠C＝90°，D是AB中点，FD⊥ED于D，BE＝，AF＝，则EF＝ 3 ．【思路引导】延长DE到H，使DH＝DE，连接FH，先证△BED≌△AHD（SAS），得AH＝BE，∠B＝∠DAH，再求出∠FAH＝90°，然后由勾股定理求出FH＝3，最后由线段垂直平分线上的性质即可得出答案．【完整解答】解：如图，延长DE到H，使DH＝DE，连接FH，∵D是AB中点，∴AD＝BD，在△BED和△AHD中，，∴△BED≌△AHD（SAS），∴AH＝BE＝，∠B＝∠DAH，∵∠C＝90°，∴∠FAH＝∠BAC+∠DAH＝∠BAC+∠B＝180°﹣90°＝90°，由勾股定理得，FH＝＝＝3，∵FD⊥ED，DE＝DH，∴EF＝FH＝3，故答案为：3．14．（2020秋•温岭市期中）如图，AD是△ABC的角平分线，DE⊥AC于点E，DF⊥AB于点F，给出下列结论：①DE＝DF；②△ADF≌△ADE；③△ABD和△ACD的面积相等．其中正确结论的序号是 ①② ．【思路引导】根据角平分线的性质和全等三角形的判定和性质解答即可．【完整解答】解：∵AD是△ABC的角平分线，DE⊥AC于点E，DF⊥AB于点F，∴DE＝DF，故①正确；在Rt△ADF与Rt△ADE中，，∴Rt△ADF≌Rt△ADE（HL），故②正确；∵得不出AB＝AC，∴△ABD和△ACD的面积无法判断相等，故③错误；故答案为：①②．15．（2019秋•南岗区校级月考）如图，在△ABC中，∠ACB＝90°，点D在边AB上，AD＝AC，点E在BC边上，CE＝BD，过点E作EF⊥CD交AB于点F，若AF＝2，BC＝8，则DF的长为 4 ．【思路引导】设∠BCD＝α，延长AC到点G，使AG＝AB，连接BG，延长EF和CA交于点H，根据已知条件证明△CEH≌△CGB，即可解决问题．【完整解答】解：设∠BCD＝α，∵∠ACB＝90°，∴∠ACD＝90°﹣α，∵AD＝AC，∴∠ADC＝∠ACD＝90°﹣α，∴∠CAB＝180°﹣2∠ACD＝2α，∴∠ABC＝90°﹣2α，∵EF⊥CD，∴∠CKF＝90°，∴∠DFK＝90°﹣（90°﹣α）＝α，∴∠CEF＝90°﹣α，如图，延长AC到点G，使AG＝AB，连接BG，∵AD＝AC，∴CD∥GB，BD＝CG＝CE，∴∠GBC＝∠BCD＝α，∴∠G＝90°﹣α，∴∠G＝∠CEF，延长EF和CA交于点H，∴∠H＝α＝∠GBC，∵∠CAB＝2α，∴∠AFH＝α，∴∠H＝∠AFH，∴AH＝AF＝2，在△CEH和△CGB中，，∴△CEH≌△CGB（ASA），∴CH＝CB＝8，∴DF＝AD﹣AF＝AC﹣AH＝CH﹣2AH＝8﹣4＝4．故答案为：4．16．（2019秋•江汉区期中）如图，AB⊥CD于点E，且AB＝CD＝AC，若点I是△ACE的角平分线的交点，点F是BD的中点．下列结论：①∠AIC＝135°；②BD＝BI；③S△AIC ＝S△BID；④IF⊥AC．其中正确的是 ①③④ （填序号）．【思路引导】如图，延长IF到G，使得FG＝FI，连接DG，BG，延长FI交AC于K．利用全等三角形的判定和性质，平行四边形的判定和性质一一判断即可．【完整解答】解：如图，延长IF到G，使得FG＝FI，连接DG，BG，延长FI交AC于K．∵AB ⊥CD ，∴∠AEC ＝90°，∴∠EAC +∠ECA ＝90°，∴∠IAC +∠ICA ＝∠EAC +∠ECA ＝45°，∴∠AIC ＝180°﹣45°＝135°，故①正确，∵AB ＝AC ，∠IAB ＝∠IAC ，AI ＝AI ，∴△AIB ≌△AIC （SAS ），∴∠AIB ＝∠AIC ＝135°，IA ＝ID ，∴∠BIC ＝360°﹣135°﹣135°＝90°，同法可证：△ICA ≌△ICD （SAS ），∴∠AIC ＝∠CID ＝135°，IA ＝ID ，∴∠AID ＝360°﹣135°﹣135°＝90°，∴∠DIB +∠AIC ＝180°，∵DF ＝FB ，IF ＝FG ，∴四边形IBGD 是平行四边形，∴ID ＝BG ＝AI ，ID ∥BG ，∴∠DIB +∠IBG ＝180°，∴∠AIC ＝∠IBG ，∵IA ＝ID ，IC ＝IB ，∴△AIC ≌△GBI （SAS ），∴∠GIB ＝∠ACI ，S △AIC ＝S △BGI ＝S 平行四边形DGBI ＝S △BDI ，故③正确，∵∠GIB +∠CIK ＝90°，∴∠CIK +∠ICK ＝90°，∴∠IKC ＝90°，即IF ⊥AC ，故④正确，不妨设BI ＝BD ，则△BDI 是等腰直角三角形，显然ID ＝IB ，即AI ＝IC ，显然题目不满足这个条件，故②错误．故答案为①③④．17．（2018秋•襄城县期末）如图，△ABC 的内角∠ABC 和外角∠ACD 的平分线相交于点E ，BE 交AC 于点F，过点E作EG∥BD交AB于点G，交AC于点H，连接AE，有以下结论：①∠BEC＝∠BAC；②△HEF≌△CBF；③BG＝CH+GH；④∠AEB+∠ACE＝90°，其中正确的结论有 ①③④ （将所有正确答案的序号填写在横线上）．【思路引导】①根据角平分线的定义得到∠EBC＝∠ABC，∠DCE＝ACD，根据外角的性质即可得到结论；②根据相似三角形的判定定理得到两个三角形相似，不能得出全等；③由BG＝GE，CH＝EH，于是得到BG﹣CH＝GE﹣EH＝GH．即可得到结论；④由于E是两条角平分线的交点，根据角平分线的性质可得出点E到BA、AC、BC和距离相等，从而得出AE为∠BAC外角平分线这个重要结论，再利用三角形内角和性质与外角性质进行角度的推导即可轻松得出结论．【完整解答】解：①BE平分∠ABC，∴∠EBC＝∠ABC，∵CE平分∠ACD，∴∠DCE＝ACD，∵∠ACD＝∠BAC+∠ABC，∠DCE＝∠CBE+∠BEC，∴∠EBC+∠BEC＝（∠BAC+∠ABC）＝∠EBC+BAC，∴∠BEC＝∠BAC，故①正确；∵②△HEF与△CBF只有两个角是相等的，能得出相似，但不含相等的边，所有不能得出全等的结论，故②错误．③BE平分∠ABC，∴∠ABE＝∠CBE，∵GE∥BC，∴∠CBE＝∠GEB，∴∠ABE＝∠GEB，∴BG＝GE，同理CH＝HE，∴BG﹣CH＝GE﹣EH＝GH，故③正确．④过点E作EN⊥AC于N，ED⊥BC于D，EM⊥BA于M，如图，∵BE平分∠ABC，∴EM＝ED，∵CE平分∠ACD，∴EN＝ED，∴EN＝EM，∴AE平分∠CAM，设∠ACE＝∠DCE＝x，∠ABE＝∠CBE＝y，∠MAE＝∠CAE＝z，如图，则∠BAC＝180°﹣2z，∠ACB＝180﹣2x，∵∠ABC+∠ACB+∠BAC＝180°，∴2y+180°﹣2z+180°﹣2x＝180°，∴x+z＝y+90°，∵z＝y+∠AEB，∴x+y+∠AEB＝y+90°，∴x+∠AEB＝90°，即∠ACE+∠AEB＝90°，故④正确；故答案为：①③④．18．（2019秋•潍坊月考）如图，△ABC中，AB＝4，AC＝7，M是BC的中点，AD平分∠BAC，过M作MF∥AD，交AC于F，则FC的长等于 5.5 ．【思路引导】可通过作辅助线，即延长FM到N，使MN＝MF，连接BN，延长MF交BA延长线于E，从而利用角之间的关系转化为线段之间的关系，进而最终可得出结论．【完整解答】解：如图，延长FM到N，使MN＝MF，连接BN，延长MF交BA延长线于E，∵M是BC中点，∴BM＝CM，∠BMN＝∠CMF，∴△BMN≌△CMF，∴BN＝CF，∠N＝∠MFC，又∵∠BAD＝∠CAD，MF∥AD，∴∠E＝∠BAD＝∠CAD＝∠CFM＝∠AFE＝∠N，∴AE＝AF，BN＝BE，∴AB+AC＝AB+AF+FC＝AB+AE+FC＝BE+FC＝BN+FC＝2FC，∴FC＝（AB+AC）＝5.5．故答案为5.5．三．解答题19．（2021春•铁岭月考）如图，在四边形ABCD中，∠B+∠ADC＝180°，CE平分∠BCD交AB于点E，连接DE．（1）若∠A＝50°，∠B＝70°，求∠BEC的度数；（2）若∠A＝∠1，试说明∠CDE＝∠DCE．【思路引导】（1）求出∠A+∠BCD＝180°，求出∠BCD，求出∠BCE，根据三角形内角和定理求出即可；（2）根据三角形内角和定理和∠A+∠BCD＝180°求出∠CDE＝∠BCE，即可得出答案．【完整解答】解：（1）∵∠A+∠B+∠BCD+∠ADC＝360°，∠B+∠ADC＝180°，∴∠A+∠BCD＝180°，∵∠A＝50°，∴∠BCD＝130°，∵CE平分∠BCD∴∠BCE＝∠BCD＝×130°＝65°，∵∠B＝70°，∴∠BEC＝180°﹣65°﹣70°＝45°，（2）证明：由（1）知∠A+∠BCD＝180°，∴∠A+∠BCE+∠DCE＝180°，∵∠CDE+∠DCE+∠1＝180°，∠1＝∠A，∴∠BCE＝∠CDE，∵CE平分∠BCD，∴∠DCE＝∠BCE，∴∠CDE＝∠DCE．20．（2021•南岗区模拟）已知：点E，F在BC上，AF＝DE，BE＝CF，∠AFE＝∠DEF．（1）如图1，求证：AB＝CD；（2）如图2，连接AC，BD，AE，DF，在不添加任何辅助线的情况下，请直接写出图2中的四组平行线．【思路引导】（1）证△ABF≌△DCE（SAS），即可得出结论；（2）由全等三角形的性质得∠B＝∠C，得AB∥CD，再证四边形ABDC是平行四边形，得AC∥BD，同理证出AF∥DE，AE∥DF．【完整解答】（1）证明：∵BE＝CF，∴BE﹣EF＝CF﹣EF，即BF＝CE，∵∠AFE＝∠DEF，∴∠AFB＝∠DEC，在△ABF和△DCE中，，∴△ABF≌△DCE（SAS），∴AB＝CD；（2）解：图2中的四组平行线为：AB∥CD，AC∥BD，AF∥DE，AE∥DF，理由如下：由（1）得：△ABF≌△DCE，∴AB＝DC，∠B＝∠C，∴AB∥CD，∴四边形ABDC是平行四边形，∴AC∥BD，∵∠AFE＝∠DEF，∴AF∥DE，∵AF＝DE，∴四边形AEDF是平行四边形，∴AE∥DF．21．（2020秋•来宾期末）如图，在五边形ABCDE中，AB＝DE，AC＝AD．（1）请你添加一个与角有关的条件，使得△ABC≌△DEA，并说明理由；（2）在（1）的条件下，若∠CAD ＝65°，∠B ＝110°，求∠BAE 的度数．【思路引导】（1）添加∠BAC ＝∠EDA ，根据SAS 即可判定两个三角形全等；（2）根据全等三角形对应角相等，运用三角形内角和定理，即可得到∠BAE 的度数．【完整解答】解：（1）添加一个角方面的条件为：∠BAC ＝∠EDA ，使得△ABC ≌△DEA ，理由如下：在△ABC 和△DEA 中，，∴△ABC ≌△DEA （SAS ），（2）在（1）的条件下，∵△ABC ≌△DEA ，∴∠ACB ＝∠DAE ，∵∠CAD ＝65°，∠B ＝110°，∴∠ACB +∠BAC ＝180°﹣∠B ＝70°，∴∠DAE +∠BAC ＝∠ACB +∠BAC ＝70°，∴∠BAE ＝∠DAE +∠BAC +∠CAD ＝70°+65°＝135°．22．（2020秋•云南期末）如图，在△ABC 中，AD 为∠BAC 的平分线，DE ⊥AB 于E ，DF ⊥AC 于F ，△ABC 面积是152cm 2，AB ＝20cm ，AC ＝18cm ，求DE 的长．【思路引导】根据S △ABC ＝S △ABD +S △ACD ，再利用角平分线的性质即可解决问题．【完整解答】解：∵AD 为∠BAC 的平分线，DE ⊥AB 于E ，DF ⊥AC 于F ，∴DE ＝DF ，∵S △ABC ＝S △ABD +S △ACD ，∴S △ABC ＝，∵△ABC 面积是152cm 2，AB ＝20cm ，AC ＝18cm ，∴152＝，∴10DE +9DF ＝152，∵DE ＝DF ，∴19DE ＝152，∴DE ＝8．23．（2021春•萧山区月考）如图，在△ABC 中，OE ⊥AB 与点E ，OF ⊥AC 与点F ，且OE ＝OF ．（1）如图①，当O 为BC 中点时，试说明AB ＝AC ；（2）如图②，当点O 在△ABC 内部，且OB ＝OC ，试判断AB 与AC 的关系．【思路引导】（1）证Rt △OBE ≌Rt △OCF （HL ），得∠B ＝∠C ，即可得出AB ＝AC ；（2）由等腰三角形的性质得∠OBC ＝∠OCB ，再证Rt △OBE ≌Rt △OCF （HL ），得∠ABO ＝∠ACO ，则∠ABC ＝∠ACB ，即可得出结论．【完整解答】（1）说明如下：∵O 为BC 中点，∴BO ＝CO ，∵OE ⊥AB ，OF ⊥AC ，∴∠OEB ＝∠OFC ＝90°，在Rt △OBE 和Rt △OCF 中，，∴Rt △OBE ≌Rt △OCF （HL ），∴∠B ＝∠C ，∴AB ＝AC ；（2）解：AB＝AC，理由如下：∵OB＝OC，∴∠OBC＝∠OCB，∵OE⊥AB，OF⊥AC，∴∠OEB＝∠OFC＝90°，在Rt△OBE和Rt△OCF中，，∴Rt△OBE≌Rt△OCF（HL），∴∠ABO＝∠ACO，∴∠ABC＝∠ACB，∴AB＝AC．24．（2021春•南山区校级期中）如图，在△ABC中，AB＝AC＝3，∠B＝40°，点D在线段BC上运动（点D不与点B、C重合），连接AD，作∠ADE＝40°，DE交线段AC于点E．（1）当∠BDA＝110°时，∠EDC＝ 30° ，∠AED＝ 70° ．（2）线段DC的长度为何值时，△ABD≌△DCE，请说明理由；（3）在点D的运动过程中，△ADE的形状可以是等腰三角形吗？若可以，求∠BDA的度数；若不可以，请说明理由．【思路引导】（1）由平角的定义和三角形外角的性质可求∠EDC，∠DEC的度数；（2）当DC＝3时，由“AAS”可证△ABD≌△DCE；（3）分AD＝DE，DE＝AE，AE＝AD三种情况讨论，由三角形内角和和三角形外角的性质可求∠BDA 的度数．【完整解答】解：（1）∵∠ADB+∠ADE+∠EDC＝180°，且∠ADE＝40°，∠BDA＝110°，∴∠EDC＝180°﹣110°﹣40°＝30°，∵AB＝AC，∴∠B＝∠C＝40°，∴∠AED＝∠EDC+∠C＝30°+40°＝70°，故答案为：30°，70°；（2）当DC＝3时，△ABD≌△DCE，理由如下：∵∠ADC＝∠B+∠BAD，∠ADC＝∠ADE+∠CDE，∠B＝∠ADE＝40°，∴∠BAD＝∠CDE，且AB＝CD＝3，∠B＝∠C＝40°，∴△ABD≌△DCE（ASA）；（3）若AD＝DE时，∵AD＝DE，∠ADE＝40°，∴∠DEA＝∠DAE＝70°，∵∠DEA＝∠C+∠EDC，∴∠EDC＝30°，∴∠BDA＝180°﹣∠ADE﹣∠EDC＝180°﹣40°﹣30°＝110°，若AE＝DE时，∵AE＝DE，∠ADE＝40°，∴∠ADE＝∠DAE＝40°，∴∠AED＝100°，∵∠DEA＝∠C+∠EDC，∴∠EDC＝60°，∴∠BDA＝180°﹣∠ADE﹣∠EDC＝180°﹣40°﹣60°＝80°，若AE＝AD时，∠AED＝∠ADE＝40°，∠DAE＝180°﹣40°﹣40°＝100°，此时D与B重合，不合题意，舍去．综上所述：当∠BDA＝80°或110°时，△ADE的形状可以是等腰三角形．25．（2021春•沂源县期末）如图，在△ABC中，∠C＝90°，AD平分∠BAC，DE⊥AB于点E，点F在AC 上，且BD＝DF．（1）求证：CF＝EB；（2）请你判断AE、AF与BE之间的数量关系，并说明理由．【思路引导】（1）根据角平分线的性质得到DC＝DE，根据直角三角形全等的判定定理得到Rt△DCF≌Rt△DEB，根据全等三角形的性质定理得到答案；（2）根据全等三角形的性质定理得到AC＝AE，根据（1）的结论得到答案．【完整解答】证明：（1）∵AD平分∠BAC，DE⊥AB，∠C＝90°，∴DC＝DE，在Rt△DCF和Rt△DEB中，，∴Rt△DCF≌Rt△DEB，∴CF＝EB；（2）AF+BE＝AE．∵Rt△DCF≌Rt△DEB，∴AC＝AE，∴AF+FC＝AE，即AF+BE＝AE．26．（2020秋•腾冲市期末）（1）某学习小组在探究三角形全等时，发现了下面这种典型的基本图形．如图1，已知：在△ABC中，∠BAC＝90°，AB＝AC，直线l经过点A，BD⊥直线l，CE⊥直线l，垂足分别为点D、E．证明：DE＝BD+CE．（2）组员小刘想，如果三个角不是直角，那结论是否会成立呢？如图2，将（1）中的条件改为：在△ABC中，AB＝AC，D、A、E三点都在直线l上，并且有∠BDA＝∠AEC＝∠BAC＝α，其中α为任意锐角或钝角．请问结论DE＝BD+CE是否成立？如成立，请你给出证明；若不成立，请说明理由．（3）数学老师赞赏了他们的探索精神，并鼓励他们运用这个知识来解决问题：如图3，过△ABC的边AB、AC向外作正方形ABDE和正方形ACFG，AH是BC边上的高，延长HA交EG于点I，求证：I是EG的中点．【思路引导】（1）由条件可证明△ABD≌△CAE，可得DA＝CE，AE＝BD，可得DE＝BD+CE；（2）由条件可知∠BAD+∠CAE＝180°﹣α，且∠DBA+∠BAD＝180°﹣α，可得∠DBA＝∠CAE，结合条件可证明△ABD≌△CAE，同（1）可得出结论；（3）由条件可知EM＝AH＝GN，可得EM＝GN，结合条件可证明△EMI≌△GNI，可得出结论I是EG 的中点．【完整解答】解：（1）如图1，∵BD⊥直线l，CE⊥直线l，∴∠BDA＝∠CEA＝90°，∵∠BAC＝90°，∴∠BAD+∠CAE＝90°∵∠BAD+∠ABD＝90°，∴∠CAE＝∠ABD在△ADB和△CEA中，，∴△ADB≌△CEA（AAS），∴AE＝BD，AD＝CE，∴DE＝AE+AD＝BD+CE；（2）DE＝BD+CE．如图2，证明如下：∵∠BDA＝∠BAC＝α，∴∠DBA+∠BAD＝∠BAD+∠CAE＝180°﹣α，∴∠DBA＝∠CAE，在△ADB和△CEA中．．∴△ADB≌△CEA（AAS），∴AE＝BD，AD＝CE，∴DE＝AE+AD＝BD+CE（3）如图3，过E作EM⊥HI于M，GN⊥HI的延长线于N．∴∠EMI＝GNI＝90°由（1）和（2）的结论可知EM＝AH＝GN∴EM＝GN在△EMI和△GNI中，，∴△EMI≌△GNI（AAS），∴EI＝GI，∴I是EG的中点．27．（2020秋•大武口区期末）如图所示，已知△ABC中，点D为BC边上一点，∠1＝∠2＝∠3，AC＝AE，（1）求证：△ABC≌△ADE；（2）若AE∥BC，且∠E＝∠CAD，求∠C的度数．【思路引导】（1）由∠1＝∠2＝∠3，可得∠1+∠DAC＝∠DAC+∠2，即∠BAC＝∠DAE，又∠1+∠B＝∠ADE+∠3，则可得∠B＝∠ADE，已知AC＝AE，即可证得：△ABC≌△ADE；（2）由题意可得，∠ADB＝∠ABD＝4x，在△ABD中，可得x+4x+4x＝180°，解答处即可；【完整解答】解：（1）∵∠1＝∠2＝∠3，∴∠1+∠DAC＝∠DAC+∠2，即∠BAC＝∠DAE，又∵∠1+∠B＝∠ADE+∠3，则可得∠B＝∠ADE，在△ABC和△ADE中，∴△ABC≌△ADE（AAS）；（2）∵AE∥BC，∴∠E＝∠3，∠DAE＝∠ADB，∠2＝∠C，又∵∠3＝∠2＝∠1，令∠E＝x，则有：∠DAE＝3x+x＝4x＝∠ADB，又∵由（1）得AD＝AB，∠E＝∠C，∴∠ABD＝4x，∴在△ABD中有：x+4x+4x＝180°，∴x＝20°，∴∠E＝∠C＝20°．28．（2020秋•船营区期末）如图，太阳光线AC与A′C′是平行的，同一时刻两根高度相同的木杆在太阳光照射下的影子一样长吗？说说你的理由．【思路引导】已知等边及垂直，在直角三角形中，可考虑AAS证明三角形全等，从而推出线段相等．【完整解答】解：影子一样长．证明：∵AB⊥BC，A′B′⊥B′C′∴∠ABC＝∠A′B′C′＝90°∵AC∥A′C′∴∠ACB＝∠A′C′B′在△ABC和△A′B′C′中，∴△ABC≌△A′B′C′（AAS）∴BC＝B′C′即影子一样长．。
研控科技MS-Mini3E总线型混合伺服驱动器用户手册说明书
目录前言 (4)1概述 (5)1.1产品介绍 (5)1.2特性 (5)1.3应用领域 (5)1.4产品命名规则 (5)2性能指标 (6)2.1 EtherCAT特性 (6)2.2电气特性 (6)2.3使用环境 (6)3安装 (7)3.1安装尺寸 (7)3.2安装方法 (7)4 驱动器端口与接线 (8)4.1接线示意图 (8)4.2端口定义 (8)4.2.1状态指示界面 (8)4.2.2旋钮拨码 (9)4.2.3状态指示灯 (9)4.2.4 EtherCAT通讯端口 (9)4.2.5控制信号输入/输出端口 (10)4.2.6编码器输入端口 (10)4.2.7电机输出端口 (10)4.2.8电源输入端口 (10)4.3输入/输出端口操作 (11)5适配电机 (14)5.1电机尺寸 (14)5.2电机规格 (17)5.3技术参数 (17)5.4电机线规格（仅适用闭环电机） (18)5.5编码器线规格（仅适用闭环电机） (18)5.6电机接线图 (19)6 EtherCAT总线 (22)6.1 EtherCAT技术原理 (22)6.2 EtherCAT数据结构 (22)6.3 EtherCAT报文寻址 (23)6.3.1 设备寻址 (24)6.3.2 逻辑寻址 (25)6.4 EtherCAT分布时钟 (25)6.5 EtherCAT通信模式 (25)6.5.1 Free Run模式 (25)6.5.2 SM2/3模式 (26)6.5.3 DC模式 (26)6.6 EtherCAT状态机 (27)6.7 应用层协议COE (27)6.7.1 COE对象字典 (28)6.7.2 服务数据对象（SDO） (28)6.7.3 过程数据对象（PDO） (28)7驱动器控制协议CiA 402 (29)7.1 CIA402状态机 (29)7.2 工作模式 (30)7.3循环同步位置模式（CSP） (31)7.4 循环同步速度模式（CSV）........................................................ 错误！未定义书签。
系列数字存储示波器使用说明书
目
录
目 录.............................................................................................................................................................. i 版权声明........................................................................................................................................................ iii 第 1 章 安全事项........................................................................................................................................... 1 1.1 常规安全事项概要..............................................................................................................................1 1.2 安全术语和符号..........................................................................................................................
C网络连接判断(最新整理)
PingReply pr = p.Send("");这句代码 进行 try catch 一下 （因为，断开网络的时候会抛出异常）；
暂停 10 分钟的那段代码要写在 catch 里，这里就不详细列出了。 你肯定知道 的。
方法1下面简程序就是可以直接去建立一控制台简用程序去简简一下不简需要简明一下程序的思路就是通简ping的方式去pinginternet上简算机的ip地址简里是ip123145681如果能ping成功代表本地简简简接上外123145681简个ip地址可以internet上的简算机的ip都可以不简如果程序的简ip比如qq163等服简器ip简简明白那个ip也可以简成如http
using System; using System.Collections.Generic; using System.Text; using workInformation; using System.Threading;
namespace ConsoleApplication1 {
13.
Console.ReadLine();
14.
}
15.
private static string CmdPing(string strIp)
16.
{
17.
Process p = new Process();
18.
p.StartInfo.FileName = "cmd.exe";
19.
eShellExecute = false;
43. }
总结，这里就是为了说明一个问题，不但是 Ping 命令，只要是命令行程序或者是 Dos 内部命令，我们都可以用上面的方式来执行它，并获取相应的结果，并且这些程序的执行 过程不会显示出来，如果需要调用外部程序就可以嵌入到其中使用了。
WCDMA中级工程师面试题
WCDMA面试题库1、了解第一代、第二代以与第三代移动通信系统的特点以与代表制式？第一代 80年代模拟APMS第二代 90年代数字GSM (CDMAIS95\TDMAIS136)第三代 IMT-2000即3G UMTS(WCDMA\CDMA2000\TD-SCDMA)目标：全球统一频段、统一标准，全球无缝覆盖；高效的频谱效率；高服务质量、高保密性能；易于2G系统演进过渡；提供多媒体业务。
车速环境：144kbps；步行环境：384kbps；室内环境：2048kbps2、掌握3G的四种典型业务以与这些业务的特征？会话型业务：语音业务和可视电话；后台类业务：数据下载、图铃下载、E-mail收发；流媒体业务：手机看电视、视频点播（VOD）、交通监控；交互类业务：在线游戏、网页浏览、定位业务；3、了解3G的三种制式以与CDMA的技术特点？WCDMA\CDMA2000\TD-SCDMA，CDMA技术是3G的核心4、掌握WCDMA RAN体系结构以与各实体之间的接口名称？5、UE的工作模式？UE有两种基本的运行模式：空闲模式和连接模式。
空闲模式：UE处于待机状态，没有业务的存在，UE和UTRAN之间没有连接，UTRAN内没有任何有关此UE的信息；通过非接入层标识如IMSI、TMSI或P-TMSI等标志来区分UE；连接模式：当UE完成RRC连接建立时，UE才从空闲模式转移到连接模式；在连接模式下，UE有4种状态： Cell-DCH, Cell-FACH, Cell-PCH, URA-PCH。
Cell-DCH：UE处于激活状态，正在利用自己专用的信道进行通信，上下行都具有专用信道，UTRAN准确的知道UE所位于的小区中；Cell-FACH：UE处于激活状态，但是上下行都只有少量的数据需要传输，不需要为此UE分配专用的信道，下行的数据在FACH上传输，上行在RACH上传输，下行需要随时监听FACH上是否有自己的信息，UTRAN准确的知道UE所位于的小区，保留了UE所使用的资源，所处的状态等信息；Cell-PCH：UE上下行都没有数据传送，需要监听PICH，以便收听寻呼，因此UE此时进入非连续接收，可有效的节电。
脑卒中国际功能残疾和健康分类简要核心组合的信度与效度研究
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基于TR069的IPTV远程升级系统的设计与实现
辑设备 ： 受管理的用户终端设备 （ Ｐ ） Ｃ Ｅ 和管理服 过 Ｒ Ｃ调用来完成某个特定功能的执行和得到返 Ｐ 务器 （ ｃ ） Ａ ｓ。在家庭网络环境下，需要从 网络侧 回的结果 。
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Ｔ ０９ Ｒ ６ 协议 的基 本思 路是 利用 了在 新 一代
ｂ Ｏ Ｐ的 Ｒ Ｃ方 法。 Ｐ Ｔ ０９ Ｒ ６ 全称为 “ Ｐ Ｃ Ｅ广域网管理协议” 。它提 Ｗｅ 服务 中广泛使 用 的基于 Ｓ Ａ
供了对下一代 网络中家庭网络设备进行 管理配置 的通用框架和协议，用于从网络侧对家庭 网络中 的网关、 路由器、 机顶盒等设备进行远程集中管理。
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在 Ｃ Ｅ中的，也可以通过 Ｄ Ｃ Ｐ Ｈ Ｐ的选项来传送给 ２１ Ｐ Ｖ 顶 盒 系统 架 构 ． Ｔ机 Ｉ ＣＥ Ｐ 。一旦 Ｃ Ｅ得到 Ａ Ｓ Ｕ Ｌ或 地 址，Ｃ Ｅ Ｐ Ｃ 的 Ｒ Ｐ
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可以在任何时候发起对 Ａ Ｓ的连接。 Ｃ
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在 Ｔ ０９所 定 义 的框 架 中，主要 包 括两 类逻 Ｒ６
等。通过这些成熟的协议 ， Ｃ 和 Ｃ Ｅ之间可以 Ａ Ｓ Ｐ 方便地 建立通信 的基本通道。Ｔ ０ ９ Ｓ Ａ 之 Ｒ６ 在 Ｏ Ｐ 上定义了用于配置、查询、升级等操作 的特定的 Ｒ Ｃ方 法，通信 的两端 （ Ｃ 和 Ｃ Ｅ Ｐ Ａ Ｓ Ｐ ）都可 以通
USB2.0与OTG规范及开发指南(全中文)(1)
改良Galveston术式在脊柱-骨盆固定融合术中的应用
３ห้องสมุดไป่ตู้ ９
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生 物 骨 科 材 料 与 临 床 研 究 ＯＲＨ ＰＥ Ｉ ＢＯ Ｅ Ｈ ＮＣ ＭＡＥＩ Ｓ Ｎ ＬＮＣ ＬＳＵ Ｙ ＴＯ Ａ ＤＣ ＩＭ Ｃ Ａ ＩＳ ＴＲ Ｌ Ａ Ｄ Ｃ ＩＩＡ ＴＤ Ａ
反应停与柳氮磺胺吡啶联合治疗强直性脊柱炎的临床研究
折 的 核 心 是 韧 带 整 复 原 理 ： 腕 部 外 周 韧 带 在 高 能 ①
动， 针道 感染 。针部骨 折 ， 晚期 塌 陷及反 射 性交 感神 经营养 障 碍 等 。我 们 的体 会 是 只要 术 中规 范 操 ｊ
作 ， 使 用 暴 力 复 位 ， 后 常 规 应 用 抗 生 素 ， 定 期 不 术 并 复 查 Ｘ 片 ， 导 患 者 合 理 进 行 功 能 锻 炼 ， 述 并 发 症 指 上
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2007版及08增补ASME规范VIII-1与04版规范制造部分的主要差别1
图UW-16.3 带螺栓连接凸缘的一些许用形式增加：非强制性附录HH 换热管胀接工艺及其评定HH-1 总则本附录为以下管子与管板胀接接头的工艺规程要求：(a) 采用附录A表A-2接头系数rf(试验)设计的接头；(b) 采用附录A表A-2接头系数rf(不试验)设计的接头；(c)管孔的有效直径取决于换热管胀接深度()0>ρ按照UHX篇设计的管板中的接头。
鉴于附录A和UHX篇不考虑胀接接头的密封性，故本附录中也不考虑。
HH-2 范围本附录中的规则适用于本附录允许的各种胀接工艺的准备及其评定。
HH-3 术语和定义与管子胀接有关的一些常见术语如下：爆炸胀——爆炸力作用在需胀接的管子的某一长度段或多个长度段上的均匀压力胀接。
槽——管孔中机加工的环形凹槽。
组合胀——先以液压胀或爆炸胀使管壁减薄到一定程度以保证管子与管孔的接触，然后采用滚柱胀接，达到管壁规定的减薄率。
液压胀——液压力作用在需胀接的管子的某一长度段或多个长度段上的均匀压力胀接。
近接触动力胀——见爆炸胀。
平行胀管器——胀杆的锥角与淬硬滚柱的锥角大致相等且方向相反的滚胀工具，从而使滚柱均匀地施压于管子表面上。
壁厚减薄百分比——因胀接而造成的管壁厚度减薄量，用管子测得的壁厚百分率表示。
前进式滚胀——分步滚压，第一步从管板的正面或接近于管板的正面开始，然后朝着管板的背面逐步推进。
普鲁塞（prosser）——见分段胀管器。
普鲁塞（prosser）胀——用分段胀管器进行胀管。
后退式滚胀——分步滚压，第一步从管板的背面或接近于管板的背面开始，然后朝着管板的正面逐步推进。
滚柱胀——将胀管工具插入到与管孔对准的管子内进行胀接。
分块胀管器——内壁为锥形的翻边厚壁圆筒沿轴向被切成若干块并用带子绑在一起。
具有与圆筒内壁锥角相反的胀杆向前推时，迫使圆筒块外伸，胀大管子。
翻边端压紧管端或管板面保持胀管器相对于管子的位置不变。
自进式滚压工具——管子滚压工具，工具上开有与其中心线成某个角度的槽，顺时针方向旋转胀杆使工具进入管子，逆时针旋转则退出。
荧光RT-PCR对乙型流感病毒爆发的检测
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德力西JD-5S 电动机综合保护器 说明书
JD-5S Series Electric Motor Integrated ProtectorUser Manual□Please carefully read this User Manual before the installationand operation of this product, and keep it properly for futurereferenceI. Overview1.1 Scope of ApplicationJD-5S series electric motor integrated protector is used in the AC 50/60Hz power supply circuit with a voltage 380V and below to form an electric motor control circuit together with the switching circuits such as AC contactor. if found abnormal working states such as open phase, overload, and stall of main circuit of electric motor, please disconnect the contact of the switching device and cut off the three-phase power supply of electric motor timely to protect the electric motor reliably. JD-5S is an upgraded product of JD-5 product, and the setting current of the protector is set directly according to the rated current marked on the nameplate of the electric motor before use for convenient operation by users; there are technologies of multiple starting timeout options and the overload protection has inverse time limit performance, the needs of various types of motors starting from light load to heavy load can be adapted. The product has functions that there is a digital tube do display the setting current value, the run and fault status light-emitting tube is used to display, and there is pointer ammeter drive output.Standard: GB/T 14048.41.2 Model definitionRated control supply voltage Us:AC220V;AC380VRated current: 1A~9.9A10A～99ASpecification codeElectric motor integrated protectors1.3 Normal working conditions and installation conditions1.3.1 Working environment: the altitude does not exceed 2000 meters; The ambient temperature is not higher than +40℃and not below than -5℃; the voltage change range of the rated control power supply is 85%-110% of the rated voltage; the product is installed in places where the medium has no serious vibration and explosion hazard, and there are no gases and dust in the medium sufficient to cause corrosion to the metals and damage to the insulation, and there is rain and snow invasion.1.3.2 Vertical or horizontal installationII. Structural Characteristics and Working PrincipleJD-5S electric motor integrated protector has protections for overload, stall, thermal memory, open phase, three-phase imbalance, and start-up timeout. This protector adopts current sensing technology, and has a relay output interface; the whole series is of the core-through type. This protector has advantages of simple structure, reliable action, and convenient operation.III. Technical ParametersRated operating current Ie range 1A~9.9A 10A~99ARated insulation voltage, Ui AC380VRated operating voltage, Ue AC380VRated control supply voltage, Us AC50/60Hz AC220V AC380VUse category Main circuit AC-3; matched auxiliary contact (body) AC-15 Shell protection grade IP40Number of types of contacts of aux.circuit1 normally openOperating voltage and operating currentunder the use category of aux. CircuitAC-15 Ue: AC220V Ie: 0.47ARated ultimate short circuit current matedSCPDRT16-00, 6ATrip level 10A, 10, 20, 30Overload protection characteristics When the actual operating current of the motor is 1.05 times of the rated operating current, the protector operation protection time is greater than or equal to 2 h; when the actual operating current rises to 1.2 times, the protector operation protection time is less than 2 h; when the actual operating current rises to 1.5 times, the protector operation protection time is less than 2 min.Range of matched DC meter head(Rated current) 0~5A (1A~4A); 0~10A (4A~10A); 0~50A (10A~40A);0~100A (40~99A)Phase open time The open time of any phase among three phases is ≤ 3s Contact capacity AC380V, 3A; AC220V, 5A (Resistive)Electrical life: ≥10 x 104 timesMechanical life ≥100 x 104 timesInstallation method Device type (with TH35 mounting rail or screw fixed installation)IV. Outline and Installation Dimensions of ProductElectric motor integrated protectorConnected to meter headConnected to meter head Notes: QA: Start Notes: QA: StartTA: Stop TA: StopKM: AC contactor 220V KM: AC contactor 380VV. Installation and Operation InstructionsInstallation and Operation Instructions:1. Please carefully read the instructions, and connect the wires according to the wiring diagram.2. 1# and 2# terminals are the working power input terminals of the protector; 3# and 4# are the normally open contacts at the control end; 5# and 6# can be connected to the pointer ammeter head. The wiring connection method can refer to the wiring diagram; three wires from the outlet end of the AC contactor are pass through three white wire holes H1, H2, and H3 of the protector to connect to the inlet wires of the electric motor (see wiring diagram).3. Operation Guide3.1 Parameter settings1) Motor rated current settingBefore starting the electric motor, power on the JD-5S protector, press the "SET" key to switch to the "Rated current" setting item, and at this time the indicator is lit and the display value on the digital tube is the setting rated current. (According to the nominal rated current value marked on the motor nameplate, the rated current is set by pressing the "" and "" add and subtract keys)2) Starting timeout protection time settingBefore starting the electric motor, power on the JD-5S protector, press the "SET" key to switch to the "Start time" setting item, and at this time the indicator is lit and the display value on the digital tube is the setting starting timeout protection time (second); set the starting timeout protection time by pressing the "" and "" add and subtract keys; when "OF" is displayed on the digital tube, this indicates that the starting timeout protection is disabled, and when the digit is displayed, this indicates that the starting timeout protection is enabled.The factory default of the product is "OF" to turn off starting timeout protection.3) Trip level settingBefore starting the electric motor, power on the JD-5S protector, and press and hold the "SET" key to switch to the "Trip level" setting item, and at this time the indicator is lit, and the digital tube displays the protection trip level to be set; if "10." is displayed, this indicates Level 10A, with "10" displayed to indicate Level 10, with "20" displayed to indicate Level 20, and with "30" displayed to indicate Level 30. By pressing the "" and "" keys, set the different trip levels. The factory default is "10." indicating Level 10A.4) Failsafe status view and status recovery:When the failsafe protection trips in the event of starting timeout, overload, open phase or unbalance in the line, the fault status indicator on the JD-5S protector panel will be lit, and at this time the protector contact opens and is locked at the OFF state; by pressing the "SET" key, the three-phase current when the trip protection works can be viewed on the external pointer ammeter. If the digital tube displays "A-", this is the trip current of phase a; if "B-" is displayed, this is the trip current of phase B; if "C-" is displayed, this is the trip current of phase C. When the line works normally, press the "RST" key to unlock the current lock state (in case of open phase, unbalance, or starting timeout, press the "RST" key for unlocking). As the overload protection has the thermal memory function, pressing the "RST" key cannot realize the unlocking action, and the unlocking will be carried out automatically when the electric motor is cooled down (also, the protector can be powered on again for unlocking).VI. Operation Precautions1. Connect the wire properly according to the wiring diagram.2. Set the setting current according to the rated current marked on the nameplate of electric motor by combining with the display on the digital tube via keys.3. During the startup of electric motor, the overload indicator will be lit. After startup, the overload indicator shall be off during normal operation, so that the adjustment process is completed.4. Please check the performance of the protector regularly, such as open phase test and overload test.5. It is strictly prohibited to increase the current of the protector when the current and electric motor or the load works abnormally, otherwise this may cause the electric motor burns.6. The equipment that may cause major economic losses or personal safety shall be designed to ensure that the technical characteristics and performance values have sufficient margins, and safety measures such as double circuit protection should be taken.VII. Common Faults and Solutions1. If the motor stops during normal operation, carefully check the electric motor for open phase or overload. First check whether the electric motor has very high temperature rise; if found temperature rise, the overload may occur; if not found temperature rise, the line may have open phase to cause trip; check whether the three-phase power supply works normally; check the moving and fixed contacts of the AC contactor have good contact; check whether three power lines of electric motor are loose; If all are normal but the electric motor still fails to start, please carefully check whether the connecting screws of the self-lock contact of AC contactor and the normally-closed contact of protector are loose; the electric motor can start only after all faults are eliminated. Do not start the product forcedly when the fault is not eliminated to prevent accidents.2. The protector works with the electric motor and the load switch (such as contactor), and the power supply shall be turned on simultaneously. If failed to realize the synchronized power-on, the protector may have open phase fault, and the electric motor cannot start normally.3. If found any product failure, please disconnect the power supply, and then find the cause of fault; after checking that the line works normally, operate the product according to the installation and operation instructions.4. For products with poor quality, please contact the local dealer company or our company.VIII. Transport and StorageThe product is not affected by rain and snow during storage and transportation, and cannot be extruded; the product shall be put in a well-ventilated environment during storage, and the relative humidity does not exceed 90% at (25℃± 5℃). The lower temperature limit is -25℃, and the upper temperature limit is +55℃.IX. Unpacking and InspectionUnpack the outer carton, and check there is a user manual in the packing box.X. Ordering NoticeThe current specification is 1A~9.9A, 10~99A. Please note that the power of electric motor shall be consist with that of the protector.When ordering, please specify the model and specification of the product. For special requirements, please contact the manufacturer.VI. Company’s CommitmentUnder the premise that users follow the use and storage conditions and the product are well sealed, within 24 months from the production date, our company will provide repair and replacement service free of charge for any damage or abnormal operation due to poor manufacture quality. A paid repair will be provided if the warranty period expires. For any damage due to one of the following situations, a paid repair will be given even if within the warranty period:(1)Improper operation, maintenance, or storage;(2)Modified and inappropriate repair without permission;(3)Damage due to falling off or during installation after purchase;(4)Force majeure such as earthquakes, fires, lightning strikes, abnormal voltages, and secondary disasters.(5)The electrical life of the product exceeds 100,000 times; the mechanical life of the product exceeds one million times.If you have any questions, please contact the dealer or our company’s customer service department.Customer Service Hotline: 400-826-8008Certificate DELIXI GROUP CO., LTD. Name: Integrated Protector for Electric Motors Model: JD-5S seriesThis product complies with the standard GB/T 14048.4, passes the inspection and is allowed to be shipped. Inspector: Check 01Inspection date: See label on inner boxManufacturer: Delixi Group Co., Ltd.Address: No. 155, Zhandong Road, Liushi Town, Yueqing City, Zhejiang Province P.C.: 325604 Tel: (86-577) 6177 8888Fax: (86-577) 6177 8000Customer Service Hotline: 400-826-8008The second edition of this User Manual was issued in Aug. 2021。
RT9271-07
1DS9271-07 April 2004Pin ConfigurationsOrdering InformationWhite LED Step-Up Converter in Tiny PackageGeneral DescriptionThe RT9271 is a step-up DC/DC converter specifically designed to drive white LEDs with a constant current.The device can drive o ne to three LEDs in series from a Li-Ion cell. Series connection of the LEDs provides identical LED currents resulting in uniform brightness and eliminating the need for ballast resistors. The RT9271switches at 1.1 MHz, allowing the use of tiny external components. The input and output capacitor can be as small as 1uF, saving space and cost versus alternative solutions. A low 0.25V feedback voltage minimizes power loss in the current setting resistor for better efficiency.The RT9271 is available in low profile SOT-26 package.FeaturesInherently Matched LED CurrentHigh Efficiency: 85% TypicalDrives Up to Three LEDs from 2.8V Supply 20V Internal SwitchFast 1.1 MHz Switching Frequency Uses Tiny 1 mm Height Inductors Requires Only 1uF Output Capacitor Low Profile SOT-26 PackageOptional 15V Over Voltage ProtectionApplicationsMobile PhoneDigital Still CameraPDAs, Handheld Computers MP3 PlayersGPS ReceiversMarking InformationFor marking information, contact our sales representative directly or through a RichTek distributor located in your area, otherwise visit our website for detail.C : Commercial StandardP : Pb Free with Commercial Standard(TOP VIEW)SOT-25LX GND FBCEOVP VCC SOT-26Functional Pin Description2DS9271-07 April 2004 Typical AppIication CircuitNote : 1. D1 is Schottky diode (SS0520).2. D2 ~ D4 are the WLED (HT-S91CW-DT) of HARVATEK.3. LX is the SH4018 series of ABC TAIWAN ELECTRONICS CORP .Figure 2. RT9271 Drivers 2 Series WLEDs Application CircuitC11uF D1SS0520LX 10uH V IN Figure 3. RT9271 Drivers 3 Series WLEDs Application CircuitC11uF D1SS0520LX 10uHV IN Figure 1. RT9271 Drivers 1 WLED Application CircuitC11uFD1SS0520LX 10uHV IN3DS9271-07 April 2004Recommended Circuits for Driving LEDsFigure 1 to Figure 3 illustrates the recommended application circuits for driving white LEDs. The series connected LEDs are driven with identical current to emit uniform luminescence, and the 250mV low reference voltage can minimize the efficiency loss across the current-sensing resistor. The recommended current setting for driving white LEDs is 10mA to 20mA, and the dimming control can be implemented by toggling CE pin with 60Hz to 1KHz PWM clock. Please refer to application notes for guidance of component selection and board layout.Function Block DiagramGNDCEOperationThe RT9271 is a constant frequency step-up converter with an internal switch. For excellent line and load regulation,the current mode control is adopted. The operations of RT9271 can be understood from block diagram clearly. The oscillator triggers the SET input of SR latch to turn on the power switch M1 at the start of each cycle. A current sense voltage sum with a stabilizing ramp is connected to the positive terminal of the PWM comparator A2. When this voltage exceeds the output voltage of the error amplifier A1, the SR latch is reset to turn off the power switch till next cycle starts. The output voltage of the error amplifier A1 is amplified from the difference between the reference voltage 0.25V and the feedback voltage. In this manner, if the error amplifiers voltage increases, more current is delivered to the output; if it decreases, less current is delivered. A 15.5V Zener diode connects from OVP pin to FB pin internally to provide an optional protection function which prevents LX pin from over-voltage damage. Especially when the case of the feedback loop broken due to component wear-out or improper connection occurs. The behavior of OVP is to clamp the output voltage to 15.5V typically. This function is suitable for the applications while driving white LEDs less than 4 in series.4DS9271-07 April 2004Note 1. Stresses beyond those listed under “Absolute Maximum Ratings ” may cause permanent damage to the device. Theseare stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability.Note 2. Devices are ESD sensitive. Handling precaution recommended. The human body model is a 100pF capacitor dischargedthrough a 1.5k Ω resistor into each pin.Note 3. The device is not guaranteed to function outside its operating conditions.Note 4. Floating the OVP pin to disable OVP function.Electrical Characteristics(V CC = 3.6V, T A = 25°C, unless otherwise specified.)Supply Voltage, V CC --------------------------------------------------------------------------------------------------−0.3V to 7V LX, OVP -----------------------------------------------------------------------------------------------------------------−0.3V to 21V The Other Pins --------------------------------------------------------------------------------------------------------−0.3V to 7V Maximum Junction Temperature ----------------------------------------------------------------------------------125°COperating Junction Temperature Range ------------------------------------------------------------------------−40°C to 125°C Lead Temperature (Soldering, 10 sec.)-------------------------------------------------------------------------260°CStorage Temperature Range ---------------------------------------------------------------------------------------−65°C to 150°CESD Susceptibility (Note 2)HBM ----------------------------------------------------------------------------------------------------------------------2kV MM ------------------------------------------------------------------------------------------------------------------------200VSupply Voltage, V CC --------------------------------------------------------------------------------------------------2.4V to 6VAbsolute Maximum Ratings (Note 1)Recommended Operating Conditions (Note 3)5DS9271-07 April 2004Efficiency vs. V IN (Driving 3 WLEDs)808182838485868788899023456V IN (V)Efficiency vs. V(Driving 2 WLEDs)808182838485868788899023456V IN (V)Efficiency vs. V IN (Driving 1 WLED)82838485868788899091922 2.53 3.54V IN (V)Typical Operating CharacteristicsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 1R e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3R e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 2Frequency vs. V IN0.70.80.911.11.21.323456V IN (V)V IN vs. Temperature22.22.42.62.83203040506070Temperature I N(°C)V FB vs. Temperature230235240245250255260010203040506070Temperature F B(°C)6DS9271-07 April 2004 Stability for Driving 3 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (500 ns/Div)V IN = 2.4V V OUT (AC)I INV LX100mA/DivStability for Driving 2 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 2Time (500 ns/Div)V IN = 3.6V V OUT (AC)I INV LX100mA/DivStability for Driving 2 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 2Time (500 ns/Div)V IN = 5.2V V OUT (AC)I INV LX 100mA/DivStability for Driving 1 WLEDR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 1Time (500 ns/Div)V IN = 2.4V V OUT (AC)I INV LX 100mA/DivStability for Driving 2 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 2Time (500 ns/Div)V IN = 2.4V V OUT (AC)I INV LX100mA/DivStability for Driving 1 WLEDR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 1Time (500 ns/Div)V IN = 3.2V V OUT (AC)I INV LX100mA/Div7DS9271-07 April 2004Stability for Driving 3 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (500 ns/Div)V IN = 6.0V V OUT (AC)I INV LX100mA/DivStability for Driving 3 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (500 ns/Div)V IN = 3.6V V OUT (AC)I INV LX 100mA/DivInrush Current for Driving 1 WLEDR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 1Time (20 us/Div)V CE = 2V V OUTI IN Frequency = 200HzV IN = 3VI IN(max) = 730mAInrush Current for Driving 2 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 2Time (20 us/Div)V CE = 2V V OUTI IN Frequency = 200HzV IN = 3.6VI IN(max) = 730mAInrush Current for Driving 3 WLEDs with soft-startR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (20 us/Div)V CE = 2VV OUTI IN Frequency = 200HzV IN = 3.6VI IN(max) = 730mAInrush Current for Driving 3 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (20 us/Div)V CE = 2VV OUTI IN Frequency = 200HzV IN = 3.6VI IN(max) = 730mA8DS9271-07 April 2004 Dimming Control for Driving 3 WLEDsR e f e r t o A p p l i c a t i o n C i r c u i t F i g u r e 3Time (20 us/Div)V C EV OUTFrequency = 200Hz V LXV IN = 3.6V9DS9271-07 April 2004Application InformationLED Current ControlThe RT9271 regulates the LED current by setting the current sense resistor (R2) connecting to feedback and ground. The internal feedback reference voltage is 0.25V.The LED current can be set from following equation easily.In order to have an accurate LED current, precision resistors are preferred (1% is recommended). The table for R2 selection is shown below.LEDI V25.02R =Dimming Controla. Using a PWM Signal to CE PinFor controlling the LED brightness, the RT9271 can perform the dimming control by applying a PWM signal to CE pin. The average LED current is proportional to the PWM signal duty cycle. The magnitude of the PWM signal should be higher than the maximum enable voltage of CE pin, in order to let the dimming control perform correctly.b. Using a DC VoltageUsing a variable DC voltage to adjust the brightness is a popular method in some applications. The dimming control using a DC voltage circuit is shown in Figure 5. According to the Superposition Theorem, as the DC voltage increases, the voltage contributed to VFB increases and the voltage drop on R2 decreases, i.e. the LED current decreases. For example, if the V DC range is from 0V to 2.8V, the selection of resistors in Figure 5 sets dimming control of LED current from 20mA to 0mA.Figure 5. Dimming Control Using a DC VoltageR2 Resistor Value SelectionC11uFLX 10uH0 to 2.8VD1SS0520V INFigure 4. PWM Dimming Control Using the CE Pin C11uFD1SS0520LX 10uHV IN Recommended Inductance and Rectifier (for Li-Ion cell)10DS9271-07 April 2004Layout GuideA full GND plane without gap break.V CC to GND noise bypass – Short and wide connection for the 1µF MLCC capacitor between Pin6 and Pin2. Minimized LX node copper area to reduce EMI.Minimized FB node copper area and keep far away from noise sources.EVB CircuitBoard Layout Example (2-Layer EVB Board)(Refer to EVB Circuit)- Top Layer -- Bottom Layer -C11uFD1SS0520LX 10uHV INVRT927111DS9271-07 April 2004Outline DimensionA1HLSOT- 25 Surface Mount PackageRT9271RICHTEK TECHNOLOGY CORP. Headquarter5F, No. 20, Taiyuen Street, Chupei City Hsinchu, Taiwan, R.O.C.Tel: (8863)5526789 Fax: (8863)5526611RICHTEK TECHNOLOGY CORP.Taipei Office (Marketing)8F-1, No. 137, Lane 235, Paochiao Road, Hsintien City Taipei County, Taiwan, R.O.C.Tel: (8862)89191466 Fax: (8862)89191465Email: marketing@12DS9271-07 April 2004A1HSOT- 26 Surface Mount Package。
电脑机的撞针问题及解决办法
电脑横机的撞针问题及解决办法推荐一: 三角部件:产生原因消除方法1: 各三角起痕严重或破裂修磨平直、光滑, 严重者重配2: 各三角之间配合不当, 间隙过大调整或重配3: 各三角热处理硬度不足重新热处理或重配, 硬度达HRC58～624: 各三角走针面发毛或碰伤修磨平滑5: 各三角平面与针床配合间隙过大镶垫三角底板, 使间隙调整至0.20～0.35mm6: 各三角平面与针床摩擦严重调整间隙或修磨三角与针床凸出部位7: 三角走针区太宽或太窄修整或调换8: 三角走针面与平面角＞90°修磨至≤90°9: 各三角螺丝松动拧紧螺丝10: 各三角装配后平面不平直修磨或配换11: 成圈三角修磨后与压针三角眉尖脱空调换戍圈三角12: 成圈三角修磨后, 成圈角＞60°修整或调换13: 压针三角眉尖撞毛或碎角修磨平直、光滑, 或调换14: 压针三角过短配换15: 起针三角与顶针三角离缝, 交接不良修正集圈高度与顶针角落差不得小于0.8mm 16: 起针三角起针角撞毛或断裂修磨或配换17: 顶针高度太高, 使织针碰塞铁调整顶针高度二: 织针1: 热处理硬度过大, 脆性调换(打闷针)2: 热处理硬度不够调换3: 钢丝舌针在弯制中针踵弯脚处应力集中调换(打闷针)4: 针踵损伤后发毛及弯曲调换三: 机头和导轨1: 使用过久, 磨损严重修整2: 螺丝松动旋紧螺丝四: 针床1: 针槽太宽修整或调换2: 使用日久, 使针槽” 坦口” 修整或调换3: 针槽起毛或损伤后有凹缺修整4: 铣槽太深或太浅修整或调换5: 针槽歪斜修整或调换6: 针槽积垢, 使针踵上翘定期揩车(易爬针)7: 针床调节螺钉未顶实或当中低校平、顶实8: 针床塞铁过紧, 压针毛纱过多修整及适当减少压针毛纱(阻尼要适当) 9: 针床塞铁过松, 压针毛纱过少调换及适当增加压针毛纱五: 其他1: 由漏针后引起的织针下坠而撞针找出漏针病因加以解决2: 由破洞和豁边后引起的织针下坠而撞针找出破洞和豁边的原因加以解决3: 喂纱梭嘴装得太低碰舌针调整喂纱点4: 针脚露出针床表面剔除针床积垢及调换5: 机头导轨螺丝松动拧紧螺丝6: 操作不当引起的撞针提高挡车工的基本功锻炼, 改进操作7: 放针高度不足改进操作, 使放针时针踵高于起针三角的起针点(如自动放针, 应检查放针机构)8: 收针退位不足或拷针不清, 毛纱挂丝引起改进操作9: 由于原料质量而引起的提高毛纱质量及准备工程中的摇(倒) 毛纱质量希望大家都能多了解一下这方面的知识。
RT-thread内核之线程调度算法
RT-thread内核之线程调度算法⼀个操作系统如果只是具备了⾼优先级任务能够“⽴即”获得处理器并得到执⾏的特点，那么它仍然不算是实时操作系统。
因为这个查找最⾼优先级线程的过程决定了调度时间是否具有确定性，例如⼀个包含n个就绪任务的系统中，如果仅仅从头找到尾，那么这个时间将直接和n相关，⽽下⼀个就绪线程抉择时间的长短将会极⼤的影响系统的实时性。
当所有就绪线程都链接在它们对应的优先级队列中时，抉择过程就将演变为在优先级数组中寻找具有最⾼优先级线程的⾮空链表。
RT-Thread内核中采⽤了基于位图(bitmap)的优先级算法（时间复杂度O(1)，即与就绪线程的多少⽆关），通过位图的定位快速的获得优先级最⾼的线程。
⼤致来说，就是每次调度的时间是恒定的：⽆论当前的系统中存在多少个线程，多少个优先级，rt-thread的调度函数总是可以在⼀个恒定的时间内选择出最⾼优先级的那个线程来执⾏。
对不同优先级的线程，RT-Thread采⽤可抢占的⽅式：即⾼优先级的线程会“⽴刻”抢占低优先级的线程。
RT-Thread内核中也允许创建相同优先级的线程。
相同优先级的线程采⽤时间⽚轮转⽅式进⾏调度（也就是通常说的分时调度器），时间⽚轮转调度仅在当前系统中⽆更⾼优先级就绪线程存在的情况下才有效。
每个线程的时间⽚⼤⼩都可以在初始化或创建这个线程时指定。
在src/scheduler.c中：rt_list_t rt_thread_priority_table[RT_THREAD_PRIORITY_MAX];//就绪线程优先级链表数组（在rt_schedule_insert_thread函数中将线程设置为就绪状态后，将当前线程链表节点插⼊对应优先级线程链表中）struct rt_thread *rt_current_thread; //保存当前运⾏的线程（在线程跳转时设置为⽬标线程to_thread）rt_uint8_t rt_current_priority; //保存当前运⾏线程优先级（在线程跳转时设置为⽬标线程to_thread的优先级）#if RT_THREAD_PRIORITY_MAX > 32/* Maximum priority level, 256 */rt_uint32_t rt_thread_ready_priority_group;//32位⼆级位图，⽤于查找⼀级位图中32个字节的最低⾮0字节（即当前所有就绪线程中最⾼优先级对应的字节）rt_uint8_t rt_thread_ready_table[32]; //256位⼀级位图，代表32个字节，分别对应256个线程优先级。
CB2包-CRISPR池化筛选分析使用Beta-Binomial测试版本1.3.4商品说明说明书
Package‘CB2’October12,2022Type PackageTitle CRISPR Pooled Screen Analysis using Beta-Binomial TestVersion1.3.4Date2020-07-23Description Provides functions for hit gene identification and quantification of sgRNA(single-guided RNA)abundances for CRISPR(Clustered Regularly Interspaced Short Palindromic Re-peats)pooled screen data analysis.Details are in Jeong et al.(2019)<doi:10.1101/gr.245571.118>and Bag-gerly et al.(2003)<doi:10.1093/bioinformatics/btg173>.Depends R(>=3.5.0)License MIT+file LICENSELazyData trueImports Rcpp(>=0.12.16),metap,magrittr,dplyr,tibble,stringr,ggplot2,tidyr,glue,pheatmap,tools,readr,parallel,R.utilsLinkingTo Rcpp,RcppArmadilloSuggests testthat,knitr,rmarkdownRoxygenNote7.1.1Encoding UTF-8VignetteBuilder knitrNeedsCompilation yesAuthor Hyun-Hwan Jeong[aut,cre]Maintainer Hyun-Hwan Jeong<************************>Repository CRANDate/Publication2020-07-2409:42:24UTCR topics documented:calc_mappability (2)Evers_CRISPRn_RT112 (3)fit_ab (3)12calc_mappability get_CPM (4)join_count_and_design (5)measure_gene_stats (5)measure_sgrna_stats (6)plot_corr_heatmap (8)plot_count_distribution (8)plot_dotplot (9)plot_PCA (10)quant (10)run_estimation (11)run_sgrna_quant (12)Sanson_CRISPRn_A375 (13)Index14 calc_mappability A function to calculate the mappabilities of each NGS sample.DescriptionA function to calculate the mappabilities of each NGS sample.Usagecalc_mappability(count_obj,df_design)Argumentscount_obj A list object is created by‘run_sgrna_quant‘.df_design The table contains a study design.Exampleslibrary(CB2)library(magrittr)library(tibble)library(dplyr)library(glue)FASTA<-system.file("extdata","toydata","small_sample.fasta",package="CB2")ex_path<-system.file("extdata","toydata",package="CB2")df_design<-tribble(~group,~sample_name,"Base","Base1","Base","Base2","High","High1","High","High2")%>%mutate(fastq_path=glue("{ex_path}/{sample_name}.fastq"))Evers_CRISPRn_RT1123 cb2_count<-run_sgrna_quant(FASTA,df_design)calc_mappability(cb2_count,df_design)Evers_CRISPRn_RT112A benchmark CRISPRn pooled screen data from Evers et al.DescriptionA benchmark CRISPRn pooled screen data from Evers et al.Usagedata(Evers_CRISPRn_RT112)FormatThe data object is a list and contains below information:count The count matrix from Evers et al.’s paper and contains the CRISPRn screening result using RT112cell-line.It contains three different replicates for T0(before)and contains different three replicates for T1(after).egenes The list of46essential genes used in Evers et al.’s study.ngenes The list of47non-essential genes used in Evers et al.’s study.design The data.frame contains study design.sg_stat The data.frame contains the sgRNA-level statistics.gene_stat The data.frame contains the gene-level statistics.Sourcehttps:///pubmed/27111720fit_ab A C++function to perform a parameter estimation for the sgRNA-level test.It will estimate two different parameters‘phat‘and‘vhat,‘and we assume input count data follows the beta-binomial distribu-tion.Dr.Keith Baggerly initially implemented this code in Matlab,and it has been rewritten it in C++for the speed-up.DescriptionA C++function to perform a parameter estimation for the sgRNA-level test.It will estimate twodifferent parameters‘phat‘and‘vhat,‘and we assume input count data follows the beta-binomial distribution.Dr.Keith Baggerly initially implemented this code in Matlab,and it has been rewritten it in C++for the speed-up.4get_CPM Usagefit_ab(xvec,nvec)Argumentsxvec a matrix contains sgRNA read counts.nvec a vector contains the library size.get_CPM A function to normalize sgRNA read counts.DescriptionA function to normalize sgRNA read counts.Usageget_CPM(sgcount)Argumentssgcount The input table contains read counts of sgRNAs for each sampleA function to calculate the CPM(Counts Per Million)(required)Valuea normalized CPM table will be returnedExampleslibrary(CB2)data(Evers_CRISPRn_RT112)get_CPM(Evers_CRISPRn_RT112$count)join_count_and_design5 join_count_and_design A function to join a count table and a design table.DescriptionA function to join a count table and a design table.Usagejoin_count_and_design(sgcount,df_design)Argumentssgcount The input matrix contains read counts of sgRNAs for each sample.df_design The table contains a study design.ValueA tall-thin and combined table of the sgRNA read counts and study design will be returned.Exampleslibrary(CB2)data(Evers_CRISPRn_RT112)head(join_count_and_design(Evers_CRISPRn_RT112$count,Evers_CRISPRn_RT112$design)) measure_gene_stats A function to perform gene-level test using a sgRNA-level statistics.DescriptionA function to perform gene-level test using a sgRNA-level statistics.Usagemeasure_gene_stats(sgrna_stat,logFC_level="sgRNA")Argumentssgrna_stat A data frame created by‘measure_sgrna_stats’logFC_level The level of‘logFC’value.It can be‘gene’or‘sgRNA’.ValueA table contains the gene-level test result,and the table contains these columns:•‘gene’:Theg gene name to be tested.•‘n_sgrna’:The number of sgRNA targets the gene in the library.•‘cpm_a’:The mean of CPM of sgRNAs within thefirst group.•‘cpm_b’:The mean of CPM of sgRNAs within the second group.•‘logFC’:The log fold change of the gene between two groups.Taking the mean of sgRNA‘logFC’s is default,and‘logFC‘is calculated by‘log2(cpm_b+1)-log2(cpm_a+1)’if‘logFC_level’parameter is set to‘gene’.•‘p_ts’:The p-value indicates a difference between the two groups at the gene-level.•‘p_pa’:The p-value indicates enrichment of thefirst group at the gene-level.•‘p_pb’:The p-value indicates enrichment of the second group at the gene-level.•‘fdr_ts’:The adjusted P-value of‘p_ts’.•‘fdr_pa’:The adjusted P-value of‘p_pa’.•‘fdr_pb’:The adjusted P-value of‘p_pb’.Examplesdata(Evers_CRISPRn_RT112)measure_gene_stats(Evers_CRISPRn_RT112$sg_stat)measure_sgrna_stats A function to perform a statistical test at a sgRNA-levelDescriptionA function to perform a statistical test at a sgRNA-levelUsagemeasure_sgrna_stats(sgcount,design,group_a,group_b,delim="_",ge_id=NULL,sg_id=NULL)Argumentssgcount This data frame contains read counts of sgRNAs for the samples.design This table contains study design.It has to contain‘group.‘group_a Thefirst group to be tested.group_b The second group to be tested.delim The delimiter between a gene name and a sgRNA ID.It will be used if onlyrownames contains sgRNA ID.ge_id The column name of the gene column.sg_id The column/columns of sgRNA identifiers.ValueA table contains the sgRNA-level test result,and the table contains these columns:•‘sgRNA’:The sgRNA identifier.•‘gene’:The gene is the target of the sgRNA•‘n_a’:The number of replicates of thefirst group.•‘n_b’:The number of replicates of the second group.•‘phat_a’:The proportion value of the sgRNA for thefirst group.•‘phat_b’:The proportion value of the sgRNA for the second group.•‘vhat_a’:The variance of the sgRNA for thefirst group.•‘vhat_b’:The variance of the sgRNA for the second group.•‘cpm_a’:The mean CPM of the sgRNA within thefirst group.•‘cpm_b’:The mean CPM of the sgRNA within the second group.•‘logFC’:The log fold change of sgRNA between two groups.•‘t_value’:The value for the t-statistics.•‘df’:The value of the degree of freedom,and will be used to calculate the p-value of thesgRNA.•‘p_ts’:The p-value indicates a difference between the two groups.•‘p_pa’:The p-value indicates enrichment of thefirst group.•‘p_pb’:The p-value indicates enrichment of the second group.•‘fdr_ts’:The adjusted P-value of‘p_ts’.•‘fdr_pa’:The adjusted P-value of‘p_pa’.•‘fdr_pb’:The adjusted P-value of‘p_pb’.Exampleslibrary(CB2)data(Evers_CRISPRn_RT112)measure_sgrna_stats(Evers_CRISPRn_RT112$count,Evers_CRISPRn_RT112$design,"before","after")8plot_count_distribution plot_corr_heatmap A function to show a heatmap sgRNA-level corrleations of the NGSsamples.DescriptionA function to show a heatmap sgRNA-level corrleations of the NGS samples.Usageplot_corr_heatmap(sgcount,df_design,cor_method="pearson")Argumentssgcount The input matrix contains read counts of sgRNAs for each sample.df_design The table contains a study design.cor_method A string parameter of the correlation measure.One of the three-"pearson", "kendall",or"spearman"will be the string.ValueA pheatmap object contains the correlation heatmaplibrary(CB2)data(Evers_CRISPRn_RT112)plot_corr_heatmap(Evers_CRISPRn_RT112$count,Ev-ers_CRISPRn_RT112$design)plot_count_distributionA function to plot read count distribution.DescriptionA function to plot read count distribution.Usageplot_count_distribution(sgcount,df_design,add_dots=FALSE)Argumentssgcount The input matrix contains read counts of sgRNAs for each sample.df_design The table contains a study design.add_dots The function will display dots of sgRNA counts if it is set to‘TRUE‘.plot_dotplot9 ValueA ggplot2object contains a read count distribution plot for‘sgcount‘.Exampleslibrary(CB2)data(Evers_CRISPRn_RT112)cpm<-get_CPM(Evers_CRISPRn_RT112$count)plot_count_distribution(cpm,Evers_CRISPRn_RT112$design)plot_dotplot A function to visualize dot plots for a gene.DescriptionA function to visualize dot plots for a gene.Usageplot_dotplot(sgcount,df_design,gene,ge_id=NULL,sg_id=NULL)Argumentssgcount The input matrix contains read counts of sgRNAs for each sample.df_design The table contains a study design.gene The gene to be shown.ge_id A name of the column contains gene names.sg_id A name of the column contains sgRNA IDs.ValueA ggplot2object contains dot plots of sgRNA read counts for a gene.Exampleslibrary(CB2)data(Evers_CRISPRn_RT112)plot_dotplot(get_CPM(Evers_CRISPRn_RT112$count),Evers_CRISPRn_RT112$design,"RPS7")10quant plot_PCA A function to plot thefirst two principal components of samples.DescriptionThis function will perform a principal component analysis,and it returns a ggplot object of the PCAplot.Usageplot_PCA(sgcount,df_design)Argumentssgcount The input matrix contains read counts of sgRNAs for each sample.df_design The table contains a study design.ValueA ggplot2object contains a PCA plot for the input.library(CB2)data(Evers_CRISPRn_RT112)plot_PCA(Evers_CRISPRn_RT112$count,Evers_CRISPRn_RT112$design) quant A C++function to quantify sgRNA abundance from NGS samples.DescriptionA C++function to quantify sgRNA abundance from NGS samples.Usagequant(ref_path,fastq_path,verbose=FALSE)Argumentsref_path the path of the annotationfile and it has to be a FASTA formattedfile.fastq_path a list of the FASTQfiles.verbose Display some logs during the quantification if it is set to‘true‘.run_estimation11 run_estimation A function to perform a statistical test at a sgRNA-level,deprecated.DescriptionA function to perform a statistical test at a sgRNA-level,deprecated.Usagerun_estimation(sgcount,design,group_a,group_b,delim="_",ge_id=NULL,sg_id=NULL)Argumentssgcount This data frame contains read counts of sgRNAs for the samples.design This table contains study design.It has to contain‘group.‘group_a Thefirst group to be tested.group_b The second group to be tested.delim The delimiter between a gene name and a sgRNA ID.It will be used if only rownames contains sgRNA ID.ge_id The column name of the gene column.sg_id The column/columns of sgRNA identifiers.ValueA table contains the sgRNA-level test result,and the table contains these columns:•‘sgRNA’:The sgRNA identifier.•‘gene’:The gene is the target of the sgRNA•‘n_a’:The number of replicates of thefirst group.•‘n_b’:The number of replicates of the second group.•‘phat_a’:The proportion value of the sgRNA for thefirst group.•‘phat_b’:The proportion value of the sgRNA for the second group.•‘vhat_a’:The variance of the sgRNA for thefirst group.•‘vhat_b’:The variance of the sgRNA for the second group.•‘cpm_a’:The mean CPM of the sgRNA within thefirst group.12run_sgrna_quant•‘cpm_b’:The mean CPM of the sgRNA within the second group.•‘logFC’:The log fold change of sgRNA between two groups.•‘t_value’:The value for the t-statistics.•‘df’:The value of the degree of freedom,and will be used to calculate the p-value of thesgRNA.•‘p_ts’:The p-value indicates a difference between the two groups.•‘p_pa’:The p-value indicates enrichment of thefirst group.•‘p_pb’:The p-value indicates enrichment of the second group.•‘fdr_ts’:The adjusted P-value of‘p_ts’.•‘fdr_pa’:The adjusted P-value of‘p_pa’.•‘fdr_pb’:The adjusted P-value of‘p_pb’.run_sgrna_quant A function to run a sgRNA quantification algorithm from NGS sampleDescriptionA function to run a sgRNA quantification algorithm from NGS sampleUsagerun_sgrna_quant(lib_path,design,map_path=NULL,ncores=1,verbose=FALSE)Argumentslib_path The path of the FASTAfile.design A table contains the study design.It must contain‘fastq_path‘and‘sample_name.‘map_path The path offile contains gene-sgRNA mapping.ncores The number that indicates how many processors will be used with a paralleliza-tion.The parallelization will be enabled if users do not set the parameter as‘-1“(it means the full physical cores will be used)or greater than‘1‘.verbose Display some logs during the quantification if it is set to‘TRUE‘ValueIt will return a list,and the list contains three elements.Thefirst element(‘count’)is a data frame contains the result of the quantification for each sample.The second element(‘total’)is a numeric vector contains the total number of reads of each sample.The last element(‘sequence’)a data frame contains the sequence of each sgRNA in the library.Sanson_CRISPRn_A37513Exampleslibrary(CB2)library(magrittr)library(tibble)library(dplyr)library(glue)FASTA<-system.file("extdata","toydata","small_sample.fasta",package="CB2")ex_path<-system.file("extdata","toydata",package="CB2")df_design<-tribble(~group,~sample_name,"Base","Base1","Base","Base2","High","High1","High","High2")%>%mutate(fastq_path=glue("{ex_path}/{sample_name}.fastq"))cb2_count<-run_sgrna_quant(FASTA,df_design)Sanson_CRISPRn_A375A benchmark CRISPRn pooled screen data from Sanson et al.DescriptionA benchmark CRISPRn pooled screen data from Sanson et al.Usagedata(Sanson_CRISPRn_A375)FormatThe data object is a list and contains below information:count The count matrix from Sanson et al.’s paper and contains the CRISPRn screening result using A375cell-line.It contains a sample of plasimd,and three biological replicates after three weeks.egenes The list of1,580essential genes used in Sanson et al.’s study.ngenes The list of927non-essential genes used in Sanson et al.’s study.design The data.frame contains study design.Sourcehttps:///pubmed/30575746Index∗datasetsEvers_CRISPRn_RT112,3Sanson_CRISPRn_A375,13calc_mappability,2Evers_CRISPRn_RT112,3fit_ab,3get_CPM,4join_count_and_design,5measure_gene_stats,5measure_sgrna_stats,6plot_corr_heatmap,8plot_count_distribution,8plot_dotplot,9plot_PCA,10quant,10run_estimation,11run_sgrna_quant,12Sanson_CRISPRn_A375,1314。