AnswersGeometry - Semester 1 PathwaysTriangle Similarity: SSS and SAS (Sec 7-3, 7-4, 7-5)

Using Triangle Similarity Theorems Answers

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1
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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
2
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Consider the two triangles.

Question illustration
A
Show that the ratios are equivalent.
Option A
B
Show that the ratios are equivalent.
Option B
C
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
Option C
D
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
Option D
3

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

Question illustration
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.
4

Which would prove that ΔABC ~ ΔXYZ? Select two options.

A
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction = StartFraction A C Over X Z EndFraction
Option A
B
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction , angle C is-congruent-to angle Z
Option B
C
StartFraction A C Over X Z EndFraction = StartFraction B A Over Y X EndFraction , Angle A is-congruent-to Angle X
Option C
D
StartFraction B A Over Y X EndFraction = StartFraction A C Over Y Z EndFraction = StartFraction B C Over X Z EndFraction
Option D
E
StartFraction B C Over X Y EndFraction = StartFraction B A Over Z X EndFraction , Angle C is-congruent-to angle X.
Option E
5

In the diagram, .

Question illustration
A
MN and SR
B
MN and QR
C
∠S ≅ ∠N
D
∠S ≅ ∠O
6

Consider the two triangles shown.

Question illustration
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.
7

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
8

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

Question illustration
A
16 units
B
20 units
C
24 units
D
28 units
9

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
10

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

Question illustration
A
15.9
B
59
C
77
D
96.8

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