Name: ______________________________
Date: _______________
Geometry: Chapter 6 Test Review
Directions: Show all work in order to receive full credit.
1. While attending a school carnival, you estimate the ratio of children to adults as
If there are 180 people at the
carnival, about how many children are in attendance?
a. about 180
b. about 150
c. about 60
d. about 120
2. The ratios of the side lengths of triangle ABC are 7:9:12 (AB:AC:BC). Solve for x.
3. A survey indicated that 5 out of 8 doctors used brand X aspirin. If 4000 doctors were surveyed, how many used
brand X?
4. If
, then ______.
a.
c.
b. ac = bd
d.
5. Which triangle is not similar to any of the others?
6. Two ladders are leaning against a wall at the same angle as shown. How long is the shorter ladder?
a. 18 ft
b. 22 ft
c. 36 ft
d. 8 ft
Tell whether each pair of triangles is similar. Explain your reasoning.
7.
Determine whether the triangles are similar. If they are, write a similarity statement.
8.
9.
10.
11.
12. In
and
In
similar, and if so, write a similarity statement.
and
State whether the triangles are
13. EXTENDED RESPONSE
Part A How do you know that
is similar to
Part B How do you know that
is similar to
Part C Find MK.
Part D Name one other triangle in the diagram that is similar to
14. Find the value of x to one decimal place.
a. 2.2
b. 22.5
c. 0.5
d. 19.0
15. If p  q, solve for x.
16. In the diagram
. Use the given side lengths to find the length of
.
17. Find AC.
18. Solve for a and b.
19. Find a, b, and h.
40
50
30
a
b
20.
Find the length of the altitude drawn to
the hypotenuse.
21. Find the value of x.
x
7
3
12
22. The geometric mean of 5 and 15 is ______.
23. Find the geometric mean of 100 and 7.
35
Geometry: Chapter 6 Test Review
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
D
6
2500 used brand X
C
A
A
Yes; The two right angles are congruent, and since parallel lines are given the alternate interior angles are
congruent, so the triangles are similar by the AA Similarity Postulate
Similar;
Not similar
Not similar
Similar;
similar,
Part A
is similar to
because the ratios of the two pairs of corresponding side lengths are equal and
the pair of included corresponding angles is congruent.
and
Part B
is similar to
because 2 pairs of corresponding angles are congruent.
because they are the same angle.
because they are both right angles.
Part C 7.2 cm; The length of the hypotenuse of
is known, 12 cm. Use the Pythagorean Theorem to find the
length of the hypotenuse of
Set up and solve a
proportion to find the length of
Part D Answers may vary. Students may name either
14. D
15. 12
16.
17.
45
75
18. a = ; b =
2
2
19. a = 12, b =
20. 6
21. 7√30
22.
23. 10√7
,h=
or