Name: ________________________ Class: ___________________ Date: __________
Similarity Item Bank from Geo Test Bank
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine whether the figures are similar.
a.
b.
c.
similar
not similar
not enough information
The polygons are similar, but not necessarily drawn to scale. Find the values ofx and y.
____
____
2.
a.
x=
b.
x=
a.
70°
11
2
11
,y=
59
c.
4
, y = 27
d.
2
3. ΔQRS ∼ ΔTUV. What is the measure of ∠V ?
b.
110°
c.
1
x = 9, y =
59
4
x = 9, y = 27
250°
d.
35°
ID: A
Name: ________________________
ID: A
Explain why the triangles are similar. Then find the value ofx.
____
4.
a.
b.
____
____
1
2
1
AA Postulate; 10
2
SSS Postulate; 10
c.
d.
2
3
2
AA Postulate; 4
3
SAS Postulate; 4
5.
1
1
c. SAS Postulate; 13
3
3
1
1
b. AA Postulate; 13
d. AA Postulate; 5
3
3
6. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram.
What is the distance between the two campsites? The diagram is not to scale.
a.
SSS Postulate; 5
a.
42.3 m
b.
47.4 m
c.
2
73.8 m
d.
82.8 m
Name: ________________________
____
ID: A
7. Use the information in the diagram to determine the height of the tree to the nearest foot.
a.
80 ft
b.
264 ft
c.
60 ft
c.
a =
d.
a =
c.
a =
d.
a =
d.
Solve for a and b.
____
____
8.
a.
a =
b.
a =
a.
a =
b.
a =
9
, b =
2
15
2
, b =
15
2
9
2
16
3
9
2
, b =
, b =
15
2
13
2
9.
400
21
400
21
, b =
, b =
580
21
20
21
3
580
21
20
21
, b =
, b =
29
21
580
21
72 ft
Name: ________________________
ID: A
____ 10. Given AE Ä BD, solve for x.The diagram is not drawn to scale.
a.
7
6
7
b.
3
2
11
c.
15
2
5
d.
26
2
5
____ 11. Find the values of x and y, given that OP Ä NQ.
a.
b.
x = 10; y = 25.5
x = 20; y = 17
c.
d.
x = 13; y = 25.5
x = 25.5; y = 10
c.
2 5
Solve for x.
____ 12.
a.
2 35
b.
2 65
4
d.
91
Name: ________________________
ID: A
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the
second. The figures are not drawn to scale.
____ 13.
a. 5 : 6 and 25 : 36
c. 5 : 6 and 36 : 49
b. 6 : 7 and 36 : 49
d. 6 : 7 and 25 : 36
____ 14. The widths of two similar rectangles are16 cm and 14 cm. What is the ratio of the perimeters? Of the areas?
a. 8 : 7 and 64 : 49
c. 9 : 8 and 81 : 64
b. 9 : 8 and 64 : 49
d. 8 : 7 and 81 : 64
____ 15. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
a.
4
3
b.
3
4
c.
5
3
d.
11
9
The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest
whole number.
____ 16. The area of the smaller trapezoid is 558 m 2 .
a.
3147 m 2
b.
3249 m 2
c.
5
576 m 2
d.
14 m 2
Name: ________________________
ID: A
Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.
____ 17.
a.
yes; 1: 3
b.
yes; 1: 2
c.
yes; 1: 5
d.
no
____ 18. Find the similarity ratio of a cube with volume729 m3 to a cube with volume 3375 m3 .
a. 81 : 225
b. 3 : 5
c. 5 : 3
d. 225 : 81
____ 19. The surface areas of two similar solids are 311 ft 2 and 1037 ft 2 . The volume of the larger solid is1755 ft 3 . What
is the volume of the smaller solid?
a.
288 ft 3
b.
1,755 ft 3
c.
961 ft 3
d.
789 ft 3
____ 20. The volumes of two similar solids are 729 m3 and 125 m 3 . The surface area of the larger solid is 324 m3 . What
is the surface area of the smaller solid?
a.
56 m 2
b.
100 m 2
c.
6
500 m 2
d.
200 m 2