Name
Class
Date
Chapter 7 Test
Form G
Do you know HOW?
Algebra Solve each proportion.
y
15
1. 4 5 20 3
6
8
2. z 2 3 5 5 27
4
3. Determine whether the polygons at the right are similar.
A
If so, write a similarity statement and give the scale factor.
If not, explain.
D
C
No; answers may vary. Sample: Only one pair of angles is
definitely congruent.
E
B
Algebra The polygons are similar. Find the value of each variable.
4.
6
3
6
5.
18
5
5
6
9
25
3
x
x
10
Determine whether the triangles are similar. If so, write a similarity statement
and name the postulate or theorem you used. If not, explain.
6.
L
M
6
6
7.
Yes; kLMN M kOPN
SAS M Theorem
X
8
9
E
6
F
12
10
G Y
16
12
No; answers may vary. Sample:
Ratios between pairs of sides are
not the same.
N
4
P
O
Z
Find the geometric mean of each pair of numbers.
9. 20 and 6 2"30
8. 8 and 12 4"6
10. Coordinate Geometry Plot A(0, 0), B(1, 0), C(1, 2), D(2, 0), and E(2, 4). Then
sketch nABC and nADE. Use SAS , to prove nABC , nADE. Sample: Check students’
AB
1
drawings; lA O lA (Reflexive Prop. of Congruence); AC
AE 5 AD 5 2
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
53
Name
Class
Date
Chapter 7 Test (continued)
Form G
11. Reasoning Name two different pairs of whole numbers that have a geometric
mean of 4. Name a pair of positive numbers that are not whole numbers that
have a geometric mean of 4. How many pairs of positive numbers have a
3
32
geometric mean of 4? Explain. Answers may vary. Sample: 1 and 16, 2 and 8; 2 and 3 ;
Algebra Find the value of x.
12.
10
15
infinitely many; any two real positive numbers whose
product is 16 will have a geometric mean of 4.
13.
5
6
24
18
x
x
8
14.
8
12
15.
6 9
6 !3
12
x
x
9
Do you UNDERSTAND?
16. Reasoning nABC , nHJK and nHJK , nXYZ. Furthermore, the ratio
between the sides of nABC and nHJK is a i b. Finally, the ratio of the sides
between nHJK and nXYZ is b i a. What can you conclude about nABC
and nXYZ? Explain.
They are congruent; they are similar by the Transitive Property. Because the
ratio of their sides is a i a, they are congruent.
17. Compare and Contrast How are Corollary 1 to Theorem 7-3 and Corollary 2
to Theorem 7-3 alike? How are they different?
Answers may vary. Sample: They both involve the altitude of right triangles and
segments of the hypotenuse. Corollary 1 involves the length of the altitude, while
Corollary 2 involves the lengths of the legs.
18. Error Analysis A student says that since all isosceles right triangles are
similar, all isosceles triangles that are similar must be right triangles. Is the
student right? Explain.
No; answers may vary. Sample: A counterexample is any pair of equilateral triangles,
which are isosceles and similar, but are not right triangles.
Determine whether each statement is always, sometimes, or never true.
19. Two equilateral triangles are similar. always
20. The angle bisector of a triangle divides the triangle into two similar triangles. sometimes
21. A rectangle is similar to a rhombus. sometimes
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
54