Analytic Geometry
Unit 1 Section 7 RECOVERY Review
Name:____________________________________
1. Triangle PQR is similar to TUS. If r = 30 cm, p = 40 cm, q = 24 cm, and s = 16.8 cm, what is the measure
of t?
A. 21 cm
B. 22.4 cm
C. 13.44 cm
D. 12.6 cm
2. The triangles shown below are similar and m a + m d = 90°. If u = 7.5 cm, v = 9 cm, w = 5 cm, and z =
6.75 cm, what is the measure of y?
A. 8.1 cm
B. 10.125 cm
C. 3.75 cm
D. 5.625 cm
3. If the scale factor of a dilation is greater than one, what happens to the resulting image?
A. The resulting image will be an enlargement of the original image.
B. The resulting image will be a reduction of the original image.
C. The resulting image will be a translation of the original image.
D. The resulting image will be a rotation of the original image.
4. In the dilation shown, the dark-colored figure represents the original image and the light-colored figure
represents the resulting image.
What is the scale factor for this dilation?
A.
B. 2
C.
D. 3
5. In the triangles below, m a + m d = 90°. Using the information given about the triangles below, determine
how the triangles can be shown to be similar.
A. The triangles are similar by SAS.
B. The triangles are similar by SSS.
C. The triangles are not similar to each other.
D. The triangles are similar by AA.
6. Which of the following represents a polygon that is six times the size of the original polygon?
A.
B.
C.
D.
7. The graph shows triangle PQR with vertices P(2,26), Q(8,14), and R(2,14) and line segment SU with
endpoints S(12,16) and U(12,12).
At what coordinates would vertex T be placed to create triangle STU, a triangle similar to triangle PQR?
A. (14,10)
B. (16,12)
C. (18,14)
D. (14,12)
8. Which statement(s) is/are true about congruent triangles?
I.
II.
III.
IV.
Each of the three pairs of corresponding sides are of equal length.
Each of the three pairs of corresponding angles are of equal measure.
Only two pairs of corresponding sides are of equal length.
Only two pairs of corresponding angles are of equal measure.
A. III and IV only
B. II only
C. I and II only
D. I only
9. Triangle EDC is similar to ADB. If AD = 12 cm, DB = 8.4 cm, AB = 17.4 cm, and ED = 7.8 cm, what is the
measure of EC?
A. 11.142 cm
B. 5.376 cm
C. 11.31 cm
D. 5.46 cm
10. In the triangles below,
CAB
EDB.
Which statement below would be sufficient to prove ABC ~ DBE?
A. DB
AB
B
B
C. DB
AB
C
C
B.
D.
11. With the information given below, determine how the triangles can be shown to be similar.
m = 16.5 in,
n = 9 in,
A. The triangles are similar by SAS.
B. The triangles are similar by SSS.
C. The triangles are similar by AA.
D. The triangles are not similar to each other.
p = 11 in,
and
q = 6 in
12. With the information given below, determine how triangle BDA can be shown to be similar to triangle CDE.
DE = 18 in,
DC = 12 in,
DB = 24 in,
and
DA = 36 in
Picture not drawn to scale.
A. The triangles are similar by SSS.
B. The triangles are not similar to each other.
C. The triangles are similar by SAS.
D. The triangles are similar by AA.
13. If the scale factor of a dilation is less than one and greater than zero, what happens to the resulting image?
A. The resulting image will be a rotation of the original image.
B. The resulting image will be a translation of the original image.
C. The resulting image will be a reduction of the original image.
D. The resulting image will be an enlargement of the original image.
14. In the dilation shown above, the dark-colored figure represents the original image and the light-colored
figure represents the resulting image.
What is the scale factor for this dilation?
A. 2
B. 4
C. 3
D. 10
15. If the figure above is dilated by a scale factor of through the origin, which of the following points
represent the coordinates of T'?
A.
B.
C.
D.
16. The graph shows triangle PQR with vertices P(0,2), Q(6,4), and R(4,0) and line segment SU with endpoints
S(4,8) and U(12,4). At what coordinates would vertex T be placed to create triangle STU, a triangle similar to
triangle PQR?
A. (18,14)
B. (16,10)
C. (14,12)
D. (16,12)
17. Triangle QRS is similar to QTU. If k = 3.6 cm, j = 3 cm, m = 2.7 cm, and f = 4.5 cm, what is the measure
of h?
A. 5.4 cm
B. 3.75 cm
C. 6 cm
D. 4.95 cm
18. With the information given below, determine how the triangles can be shown to be similar.
a = 17.5 in
e = 7 in
A. The triangles are not similar to each other.
B. The triangles are similar by SSS.
C. The triangles are similar by AA.
D. The triangles are similar by SAS.
b = 14 in
f = 7 in
c = 10 in
g = 4 in
19. If the circle above is dilated using a scale factor of 8, what will be the radius of the resulting circle?
A.
B.
C.
D.
units
units
units
units
20. In the figure below, m A = m F = 79°. Also, m C = 42° and m D = 69°. Determine how the triangles
can be shown to be similar.
A. The triangles are similar by SAS.
B. The triangles are not similar to each other.
C. The triangles are similar by AA.
D. The triangles are similar by SSS.
21. With the information given below, determine how the triangles can be shown to be similar.
e = 4 in
h = 12 in
f = 3 in
i = 9 in
g = 5 in
j = 15 in
A. The triangles are not similar to each other.
B. The triangles are similar by SAS.
C. The triangles are similar by AA.
D. The triangles are similar by SSS.
22. If rectangle QRST is dilated by a scale factor of 9 through the origin, which of the following points
represent the coordinates of Q'?
A. (3,-9)
B. (-27,9)
C. (27,-9)
D. (27,-1)
23. With the information given below, determine how the triangles can be shown to be similar.
a = 15 in
x = 5 in
b = 12 in
y = 4 in
c = 9 in
z = 3 in
A. The triangles are similar by SAS.
B. The triangles are similar by SSS.
C. The triangles are not similar to each other.
D. The triangles are similar by AA.
24. With the information given below, determine how the triangles can be shown to be similar.
a = 14 in,
b = 12 in,
d = 7 in,
and
e = 6 in
A. The triangles are similar by AA.
B. The triangles are similar by SAS.
C. The triangles are similar by SSS.
D. The triangles are not similar to each other.
25. With the information given on the triangles below, determine how triangle QRS and triangle QTU can be
shown to be similar.
A. The triangles are similar by SSS.
B. The triangles are similar by AA.
C. The triangles are not similar to each other.
D. The triangles are similar by SAS.
26. In the triangles below, m is congruent to n. Using the information given on the triangles below,
determine how the triangles can be shown to be similar.
A. The triangles are similar by SAS.
B. The triangles are similar by SSS.
C. The triangles are similar by AA.
D. The triangles are not similar to each other.
27. With the information given below, determine how triangle LMN can be shown to be similar to triangle LOP.
LM is two-thirds the length of LO and MN is two-thirds the length of OP.
A. The triangles are not similar to each other.
B. The triangles are similar by SAS.
C. The triangles are similar by SSS.
D. The triangles are similar by ASA.
Answers
1. B
2. C
3. A
4. A
5. D
6. D
7. D
8. C
9. C
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
B
A
C
C
A
A
D
D
A
B
C
D
C
B
B
B
C
B