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Triangle Similarity: SSS and SAS Answers

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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
2
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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.
3

Triangles O N M and S R Q are shown. Angles O N M and S R Q are congruent. The length of side N M is 10 and the length of side S R is 20. The length of side N O is 8 and the length of side Q R is x.

Question illustration
A
16
B
20
C
25
D
50
4

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
5

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
6

△RST ~ △RYX by the SSS similarity theorem.

Question illustration
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
7

2 triangles are shown. The first triangle has side lengths x, x, 50. The second triangle has side lengths 45, 45, 75.

Question illustration
A
1.5
B
20
C
30
D
67.5
8

In the diagram, .

Question illustration
A
MN and SR
B
MN and QR
C
∠S ≅ ∠N
D
∠S ≅ ∠O
9

In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.

Question illustration
A
HF is 2 units and GH is 3 units.
B
HF is 3 units and GH is 2 units.
C
HF is 4 units and GH is 2 units.
D
HF is 3 units and GH is 4 units.
10

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

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Triangle Similarity: SSS and SAS Answers — OC27…