Similar Triangles Quiz
Questions: 16 · 10 minutes
1. A triangle has vertices (1,1), (3,1), and (1,2). Which set gives its image after a dilation centered at the origin with scale factor 2?
(1,1), (5,1), and (1,3)
(2,2), (4,2), and (2,3)
(2,2), (6,2), and (2,4)
(3,3), (5,3), and (3,4)
2. Which statement must be true when two triangles are similar?
The triangles have equal perimeters, and one pair of angles is equal.
Corresponding angles are equal, and corresponding side lengths are identical.
The triangles have equal areas, but their corresponding angles may differ.
Corresponding angles are equal, and corresponding side lengths are proportional.
3. Two triangles each have a pair of sides in the ratio 2:3 and one equal angle, but the equal angle is not between the compared sides. What can be concluded from this information alone?
The triangles are similar by SAS.
There is not enough information to guarantee similarity.
The triangles are similar by AA.
The triangles are congruent by SAS.
4. Given △ABC ∼ △DEF, angle A corresponds to angle D. If angle B is 68° and angle C is 47°, what is the measure of angle D?
47°
68°
65°
115°
5. At the same time of day, a 1.8 m person casts a 1.2 m shadow, while a tree casts an 8 m shadow. Assuming the sun creates similar triangles, how tall is the tree?
9.6 m
12 m
14.4 m
18 m
6. In △ABC, points D and E lie on AB and AC, and DE is parallel to BC. If AD = 6, DB = 3, AE = 8, and EC = x, what is x?
4
3
6
2
7. Which information is not sufficient by itself to prove that two triangles are similar?
One pair of corresponding angles is equal.
Two pairs of corresponding angles are equal.
All three pairs of corresponding sides are proportional.
Two pairs of corresponding sides are proportional and their included angles are equal.
8. Which similarity criterion uses two pairs of equal corresponding angles?
AA similarity
SSS similarity
SAS similarity
The Pythagorean theorem
9. A larger triangle is similar to a smaller triangle with a length scale factor of 2.5. If the smaller triangle's perimeter is 18 units, what is the larger triangle's perimeter?
36 units
112.5 units
50.5 units
45 units
10. A side measuring 15 cm in one triangle corresponds to a 9 cm side in a second similar triangle. What is the length scale factor from the first triangle to the second?
5/3
3/5
2/5
5/2
11. A triangle has side lengths 3, 4, and 5. A similar triangle has a shortest side of 6. What is the longest side of the second triangle?
8
9
12
10
12. In △ABC, D lies on AB, E lies on AC, and DE is parallel to BC. Why are △ADE and △ABC similar?
They have the same area.
Parallel lines create equal corresponding angles, so AA similarity applies.
They share all three side lengths.
Any triangle inside another triangle is similar to it.
13. A student claims that triangles with side lengths 5, 7, 9 and 10, 14, 17 are similar. What is the best evaluation of the claim?
The claim is correct because two side pairs have a ratio of 2.
The claim is correct because both sets satisfy the triangle inequality.
The claim is incorrect because similar triangles must have equal side lengths.
The claim is incorrect because 17/9 is not equal to the scale factor of 2 shown by the other side pairs.
14. If △ABC ∼ △DEF in the stated order, which side corresponds to BC?
EF
DE
DF
AB
15. Which pair of side-length sets could belong to similar triangles?
4, 6, 8 and 8, 10, 16
4, 6, 8 and 6, 8, 12
4, 6, 8 and 6, 9, 12
4, 6, 8 and 5, 7.5, 11
16. A triangle has an area of 7 square units. A similar triangle has corresponding side lengths three times as long. What is its area?
21 square units
42 square units
63 square units
147 square units