可汗学院数学题目-36Congruenceandsimilarity
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Congruence and similarity
1.
In the figure above,BC and AD are parallel. What is the length, in centimeters(cm), of BF?
Correct answer: 10 Level: 3
2.
Note: figure not drawn to scale
Triangles JKL and RST are shown above. Angles are given in radians, to the nearest hundredth. What is the value of θ in radians, to the nearest tenth?
Correct answer: 1.3 Level: 3
3.
In the diagram above, triangle AFG is similar to triangle ABC. What is the measure of∠AGF, in degrees?
Correct answer: 78 Level: 3
In the diagram at left, suppose a=23
x . What is the measure of x ?
Correct answer: 54° Level: 3
5. In the diagram at left,
AD
is congruent to BD . Which of the following statements is true?
A. AE bisects ∠CAB
B. ∠ACB is congruent to ∠ABC
C. triangle ABC is isosceles
D. AE is a median of △ABC
Correct answer: C Level: 3
The diagram at left shows four lines:AB,CD,AD, and BC. Which of the following statements is true?
A.∠ABC measures88°
B.∠BCD measures80°
C.AD intersects BC
D.AD is parallel to BC
Correct answer: C Level: 4
7.In the diagram at left,AB is
congruent to BC. Which of the
following statements is true?
A.∠DAC is congruent to∠
DCA
B.∠BAC is congruent to∠
BCA
C.∠ABC is congruent to∠
ADC
D.∠BAD is congruent to∠
BCD
Correct answer: B Level: 4
Isosceles triangles ABC and DEF shown above are similar triangles. The length AB equals the length BC, and the length DE equals the length EF. What is the value of v in radians, to the nearest hundredth?
Correct answer: 2.09 Level: 4
9.
Given the lengths of the segments in the figure above, what is the length, to the nearest
tenth, of n ?
Correct answer: 42
5Level: 4
10.
In the figure at left, lines c and d are parallel. What is the value of x?
Correct answer: 8 Level: 4
11.
Note: figure not drawn to scale
Parallelogram ABCD shown above is congruent to parallelogram PQRS. What is the value of a in radians, to the nearest hundredth?
Correct answer: 0.39 Level: 4
12.
The diagram at left shows a rectangular billiard table with a width of39inches (in)and a length of78 in. A player is trying to shoot the red ball located at point H, into the corner pocket D by bouncing the ball off of a point R that is x inches from point B. The player knows that when the ball bounces off point R,∠HRB will be congruent to∠DRC. If the point B B is the midpoint of AC and the red ball is15in above B, approximately what is the value of x?
A.7in
B.9in
C.11in
D.13in
Correct answer: C Level: 4