AnswersAZ-Geometry A MA201Triangle Similarity: SSS and SAS (Sec 7-3, 7-4, 7-5)

Week 8: Proving Triangles Similar Answers

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2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.

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A
15.9
B
59
C
77
D
96.8
2
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△RST ~ △RYX by the SSS similarity theorem.

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A
StartFraction X Y Over T S EndFraction
Option A
B
StartFraction S Y Over R Y EndFraction
Option B
C
StartFraction R X Over X T EndFraction
Option C
D
StartFraction S T Over Y X EndFraction
Option D
3

In the diagram, AB is 6 units, BC is 30 units, and AE is 4 units.

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A
16 units
B
20 units
C
24 units
D
28 units
4

Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.

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A
The triangles are not similar, but they are congruent.
B
The triangles are neither similar nor congruent.
C
The triangles are similar by the SAS similarity theorem.
D
The triangles are similar by the SSS similarity theorem.
5

Consider the two triangles shown.

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A
The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
B
The given sides and angles can be used to show similarity by the SSS similarity theorem only.
C
The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D
The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.
6

The ratios of corresponding sides in the two triangles are equal.

Question illustration
A
∠F ≅ ∠J
B
∠I ≅ ∠F
C
∠E ≅ ∠H
D
∠G ≅ ∠I
7

Below are statements that can be used to prove that the triangles are similar. 1. 2. ∠B and ∠Y are right angles.3.?4.?Which two statements are missing in steps 3 and 4?

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A
∠X ≅ ∠C△ABC ~ △ZYX by the SAS similarity theorem.
B
∠B ≅ ∠Y△ABC ~ △ZYX by the SAS similarity theorem.
C
= 2△ABC ~ △ZYX by the SSS similarity theorem.
Option C
D
= 2△ABC ~ △ZYX by the SSS similarity theorem.
Option D
8

In the diagram, .

Question illustration
A
J measures 60°.
Option A
B
J measures 30°.
Option B
C
I measures 60°.
Option C
D
I measures 30°.
Option D
9

In the diagram, .

Question illustration
A
MN and SR
B
MN and QR
C
∠S ≅ ∠N
D
∠S ≅ ∠O
10

Consider the two triangles.

Question illustration
A
Show that the ratios are equivalent, and ∠U ≅ ∠X.
Option A
B
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
Option B
C
Show that the ratios are equivalent, and ∠W ≅ ∠X.
Option C
D
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
Option D

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