Using Triangle Similarity Theorems Answers
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1
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△RST ~ △RYX by the SSS similarity theorem.
A
StartFraction X Y Over T S EndFraction
B
StartFraction S Y Over R Y EndFraction
C
StartFraction R X Over X T EndFraction
D
StartFraction S T Over Y X EndFraction
2
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In the diagram, .
A
MN and SRB
MN and QRC
∠S ≅ ∠ND
∠S ≅ ∠O3
Consider the two triangles shown.
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.4
Consider the two triangles.
A
Show that the ratios are equivalent.
B
Show that the ratios are equivalent.
C
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
D
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
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
B
StartFraction B A Over Y X = StartFraction B C Over Y Z EndFraction , angle C is-congruent-to angle Z
C
StartFraction A C Over X Z EndFraction = StartFraction B A Over Y X EndFraction , Angle A is-congruent-to Angle X
D
StartFraction B A Over Y X EndFraction = StartFraction A C Over Y Z EndFraction = StartFraction B C Over X Z EndFraction
E
StartFraction B C Over X Y EndFraction = StartFraction B A Over Z X EndFraction , Angle C is-congruent-to angle X.
6
In the diagram, .
A
J measures 60°.
B
J measures 30°.C
I measures 60°.D
I measures 30°.7
Consider the two triangles.
A
LM is 3 units and XZ is 5 units.B
LM is 4 units and XZ is 6 units.C
LM is 5 units and XZ is 3 units.D
LM is 6 units and XZ is 4 units.8
2 triangles are shown. The first triangle has side lengths x, x, 50. The second triangle has side lengths 45, 45, 75.
A
1.5B
20C
30D
67.59
The ratios of corresponding sides in the two triangles are equal.
A
∠F ≅ ∠JB
∠I ≅ ∠FC
∠E ≅ ∠HD
∠G ≅ ∠I10
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?
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.
D
= 2△ABC ~ △ZYX by the SSS similarity theorem.
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