Ratio and Proportionppt71,比和proportionppt

Find and simplify the ratio of two numbers.
Use proportions to solve real-life problems, such as computing the width of a painting.
Chapter 8 Definitions Ch.8 Postulates/
SOLUTION:
DE is twice AB and DE = 8, so AB = ½(8) = F
4
Use the Pythagorean Theorem to determine what side BC is.
DF is twice AC and AC = 3, so DF = 2(3) =
4m
18 in
Solution: To simplify the ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible.
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Ex. 1: Simplifying Ratios
Simplify the ratios:
a. 12 cm
b. 6 ft
4 cm
18 ft
c. 9 in. 18 in.
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Ex. 1: Simplifying Ratios
Simplify the ratios:
a. 12 cm
b. 6 ft
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Ex. 1: Simplifying Ratios
Simplify the ratios:
a. 12 cm
4m
12 cm
12 cm 12
3
4m
4∙100cm
400
100
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Ex. 1: Simplifying Ratios
Simplify the ratios:
b. 6 ft
18 in
6 ft
Theorems
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3two quantities that are measured in the same units, then the ratio of a to be is a/b. The ratio of a to be can also be written as a:b. Because a ratio is a quotient, its denominator cannot be zero. Ratios are usually expressed in simplified form. For instance, the ratio of 6:8 is usually simplified to 3:4. (You divided by 2)
6x = 180 x = 30
Reason Triangle Sum Theorem Combine like terms Divide each side by 6
So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.
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Ex. 4: Using Ratios
So, ABCD has a length xof 1=8 6centimDeitevris daned ea awcidhthsoifd1e2 cbmy. 10
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Ex. 3: Using Extended Ratios
The measures of the angles in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles.
6∙12 in
72 in.
4
18 in
18 in.
18 in.
4 1
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Ex. 2: Using Ratios
The perimeter of rectangle
ABCD is 60 centimeters.
B
C
The ratio of AB: BC is 3:2.
Find the length and the
w
width of the rectangle
A
l
D
h
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Ex. 2: Using Ratios
SOLUTION:
Because the
ratio of AB:BC is 3:2, you
B
C
can represent the length of
AB as 3x and the width of
w
BC as 2x.
8.1 Ratio and Proportion
Geometry
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Objective & DFA
Objective:SWBAT write & solve proportions.
DFA: pp.368-369 - #8 & #20
HW: pp.368-371 (2-46 even)
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Objectives/Assignment
A
l
D
h
10
Solution:
Statement
Reason
2l + 2w = P Formula for perimeter of a rectangle
2(3x) + 2(2x) = 60 Substitute l, w and P
6x + 4x = 60 Multiply
10x = 60 Combine like terms
The ratios of the side lengths of ∆DEF to the F corresponding side lengths of ∆ABC are 2:1. Find the unknown lengths.
C
3 in.
A
B
D
8 in.
E
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Ex. 4: Using Ratios
Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°.
x°
J
h
K
2x°
3x°
L
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Solution:
Statement x°+ 2x°+ 3x° = 180°