Question

The two triangles below are similar.
mc004-1.jpg

What is the ratio of the corresponding side lengths?
4:9
4:2
26:26
4.5:2

Answer 1

Which statements about the relationship between the two triangles below are true? Check all that apply.

Triangle A C D. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle R S T. Angle R is 74.9 degrees and angle S is 45.1 degrees.
Angle C is congruent to angle T
Angle C is congruent to angle S
Angle D is congruent to angle T
Triangle D C A is congruent to triangle T S R
Triangle D C A is similar to triangle T S R
Triangle C A D is similar to triangle T R S
Triangle C A D is congruent to triangle T R S

Answer 2

Which best explains the relationship between the two triangles below?

Triangle D C A. Angle D is 51.2 degrees and angle A is 96.5 degrees. Triangle S R T. Angle S is 32.3 degrees and angle R is 96.5 degrees.
Triangle A D C is similar to triangle R T S because Angle A is congruent to angle R, Angle C is congruent to angle S, and Angle D is congruent to angle T.
Triangle A D C is similar to triangle R T S because Angle A is similar to angle R, Angle C is similar to angle S, and Angle D is similar to angle T.
Triangle A D C is not similar to Triangle R T S because Angle D is not congruent to Angle S.
Triangle A D C is not similar to Triangle R T S because C D less than S T, D A less than T R, and C A less than S R.

Answer 3

The triangles shown are similar. Which side of triangle PQR corresponds to side LN in triangle MNL?

Triangle L N P. Side L N is 12, N M is 10, M L is 14. Triangle P R Q. Side P R is 28, R Q is 24, Q P is 20.
RQ
PQ
PR
LM

Answer 4

Lorie correctly determines that for the triangles below, the statement Triangle N M O is similar to triangle T S R and the statement Triangle N M O is similar to triangle T R S both describe the relationship between the two triangles.

Triangle M N O. Angle M is 54.4 degrees and angle N is 71.2 degrees. Triangle R S T. Angle R is 54.4 degrees and angle T is 71.2 degrees.

Which best describes why both similarity statements are correct?
Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S.
Each triangle has two similar angles: Angle M is similar to angle O and Angle R is similar to angle S.
The triangles each have two given angle measures and one unknown angle measure.
All statements, regardless of the order of the vertices, define the same triangles.

Answer 5

Which best describes the relationship between the two triangles below?
Triangle M N L. Angle M is 51 degrees and angle L is 36 degrees. Triangle F H G. Angle F is 51 degrees and angle G is 36 degrees.
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the third angle is unknown.
Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the side lengths are unknown.

Answer 6

The triangles below are similar.

Triangle A B C. Side A C is 10 and side A B is 5. Angle C is 30 degrees. Triangle D E F. Side E D is 7.5 and side D F is 25. Angle F is 30 degrees and angle E is 90 degrees.

Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle C B A is similar to triangle F E D
Triangle C B A is similar to triangle F D E
Triangle B A C is similar to triangle E F D
Triangle B A C is similar to triangle E D F
Triangle A B C is similar to triangle D E F
Triangle A B C is similar to triangle D F E

Answer 7

Using side lengths only, could the triangles be similar?

Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.
Yes, StartFraction 0.5 Over 1 EndFraction = StartFraction 0.5 Over 1 EndFraction.
Yes, One-half = StartFraction 0.5 Over 1 EndFraction.
Yes, StartFraction 1.5 Over 1 EndFraction = StartFraction 2 Over 1.5 EndFraction.

Answer 8

The triangles below are similar.

Triangle G H F. Angle G is 65 degrees, H is 24 degrees, F is 91 degrees. Triangle J K L. Angle J is 24 degrees, K is 91 degrees, L is 65 degrees.

Which similarity statement expresses the relationship between the two triangles?
Triangle F G H is similar to Triangle K L J
Triangle F G H is congruent to Triangle K L J
Triangle F G H is similar to triangle J K L
Triangle F G H is similar to triangle J K L

Answer 9

Shelly states that the triangles below are similar. Which proportion supports her statement?

Triangle S T R. Side S T is 6, T R is 4, R S is 8. Triangle N M O. Side O N is 15, N M is 20, M O is 10.
StartFraction 8 Over 4 EndFraction = StartFraction 15 Over 10 EndFraction
StartFraction 8 Over 10 EndFraction = StartFraction 4 Over 20 EndFraction
StartFraction 6 Over 4 EndFraction = StartFraction 20 Over 10 EndFraction
StartFraction 8 Over 6 EndFraction = StartFraction 20 Over 15 EndFraction

Answer 10

Julia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M.

Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees.

Which best describes the accuracy of Julia’s solution?
Accurate. The triangles are similar and the congruent angles are listed in corresponding order.
Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º.
Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.
Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G.

Answer 11

Mikel is determining if the two triangles below could be similar based on their side lengths.

Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 8 centimeters. Triangle W X U. Side W X is 18 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters.

Which statements accurately describe the triangles? Check all that apply.
The common ratio between the triangles is 3 because StartFraction 18 Over 6 EndFraction = 3.
The common ratio between the triangles is 2.5 because StartFraction 7.5 Over 3 EndFraction = 2.5.
The triangles could be similar.
The triangles could not be similar.
The ratios of the side lengths are not consistent.
The ratios of the side lengths are consistent.
0

Answer 12

4:9

Answer 13

- Angle C is congruent to angle T
- Triangle DCA is similar to triangle TSR
- Triangle CAD is similar to triangle TRS

Answer 14

Triangle A D C is similar to triangle R T S because Angle A is congruent to angle R, Angle C is congruent to angle S, and Angle D is congruent to angle T.

Answer 15

PR

Answer 16

Each triangle has two similar angles: Angle M is similar to angle O and Angle R is similar to angle S.

Answer 17

Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.

Answer 18

Triangle A B C is similar to triangle D E F.

Answer 19

No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.

Answer 20

Triangle F G H is similar to triangle J K L.

Answer 21

StartFraction 8 Over 4 EndFraction = StartFraction 15 Over 10 EndFraction.

Answer 22

Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order.

Answer 23

The triangles could be similar and the ratios of the side lengths are consistent. (3/2)