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Triangle Similarity — Test Answers

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21
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What is the value of x ?

A
25 units
B
12 units
C
15 units
D
20 units
22
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Which transformations could have occurred to map triangle ABC to triangle cap A double prime cap b double prime cap c double prime ?

A
a rotation and a reflection
B
a reflection and a dilation
C
a dilation and a rotation
D
a translation and a dilation
24

What is the value of y ?

A
6 square root of 3 units
B
9 square root of 3 units
C
12 square root of 3 units
D
3 square root of 3 units
26

Which transformations could have occurred to map triangle ABC to triangle cap A double prime cap b double prime cap c double prime ?

A
a rotation and a dilation
B
a reflection and a dilation
C
a rotation and a reflection
D
a translation and a dilation
27

Why is the information in the diagram enough to determine that triangle LMN approximates triangle PON using a rotation about point cap n and a dilation?

A
because both triangles appear to be equilateral
B
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
C
because one pair of congruent corresponding angles is sufficient to determine similar triangles
D
because angle MNL and angle ONP are congruent angles
29

To prove that triangle cap d cap f cap e approximates triangle cap g cap f cap h by the SAS similarity theorem, it can be stated that the fraction with numerator cap d cap f and denominator cap g cap f is equal to the fraction with numerator cap e cap f and denominator cap h cap f and

A
angle cap d cap f cap e is 4 times greater than angle cap g cap f cap h .
B
angle cap f cap h cap g is 1 fourth the measure of angle cap f cap e cap d .
C
angle cap d cap f cap e is congruent to angle cap g cap f cap h .
D
angle cap f cap h cap g is congruent to angle cap e cap f cap d .
30

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles are congruent and therefore similar, with side lengths in a ratio of 1 to 1 ratio.
B
All equilateral triangles can be mapped onto each other using dilations.
C
All equilateral triangles can be mapped onto each other using rigid transformations.
D
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
31

To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

A
angle cap c is congruent to angle cap g .
B
the fraction with numerator cap A cap c and denominator cap g cap i is equal to the fraction with numerator cap h cap i and denominator cap b cap c .
C
angle cap c is congruent to angle cap c .
D
the fraction with numerator cap A cap c and denominator cap g cap i is equal to the fraction with numerator cap b cap c and denominator cap h cap i .
32

Which composition of transformations will create a pair of similar, not congruent triangles?

A
a translation, then a rotation
B
a reflection, then a translation
C
a rotation, then a reflection
D
a rotation, then a dilation
33

Which statements are true? Choose two correct answers.

A
triangle AXC approximates triangle CXB
B
triangle ACB approximates triangle AXC
C
triangle BCX is congruent to triangle ACX
D
triangle CXA is congruent to triangle CBA
E
triangle ABC is congruent to triangle BXC
34

What is the value of x ?

A
25 units
B
20 units
C
15 units
D
12 units
35

Select the correct similarity statement.

A
triangle STR approximates triangle TQR
B
triangle STR approximates triangle SQR
C
triangle STR approximates triangle RST
D
triangle STR approximates triangle RTQ
38

If the triangles are similar, which must be true?

A
the fraction with numerator cap r cap y and denominator cap r cap x is equal to the fraction with numerator cap r cap s and denominator cap r cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
B
the fraction with numerator cap r cap y and denominator cap r cap s is equal to the fraction with numerator cap r cap x and denominator cap r cap t is equal to the fraction with numerator cap r cap s and denominator cap r cap y
C
the fraction with numerator cap r cap y and denominator cap y cap s is equal to the fraction with numerator cap r cap x and denominator cap x cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
D
the fraction with numerator cap r cap y and denominator cap r cap s is equal to the fraction with numerator cap r cap x and denominator cap r cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
39

Which would prove that triangle cap A cap b cap c approximates triangle cap x cap y cap z ? Choose two correct answers.

A
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap A cap c and denominator cap y cap z is equal to the fraction with numerator cap b cap c and denominator cap x cap z
B
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z is equal to the fraction with numerator cap A cap c and denominator cap x cap z
C
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z comma angle cap c is congruent to angle cap z
D
the fraction with numerator cap A cap c and denominator cap x cap z is equal to the fraction with numerator cap b cap A and denominator cap y cap x comma angle cap A is congruent to angle cap x
E
the fraction with numerator cap b cap c and denominator cap x cap y is equal to the fraction with numerator cap b cap A and denominator cap z cap x comma angle cap c is congruent to angle cap x
40

Why is the information in the diagram enough to determine that triangle LMN approximates triangle PON using a rotation about point cap n and a dilation?

A
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
B
because both triangles appear to be equilateral
C
because angle MNL and angle ONP are congruent angles
D
because one pair of congruent corresponding angles is sufficient to determine similar triangles

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