Triangle Similarity — Test Answers

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1
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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 c .
B
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 .
C
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 .
D
angle cap c is congruent to angle cap g .
3

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 combinations of dilations and rigid transformations.
C
All equilateral triangles can be mapped onto each other using dilations.
D
All equilateral triangles can be mapped onto each other using rigid transformations.
4

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 dilation and a rotation
C
a reflection and a dilation
D
a translation and a dilation
6

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 congruent to 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 4 times greater than 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 .
7

What is the perimeter of triangle WXY ?

A
11 point 5 7 cm
B
12 point 2 2 cm
C
14 point 5 0 cm
D
12 point 4 6 cm
8

What is AX ?

A
6 units
B
8 units
C
2 units
D
4 units
9

How can the triangles be proven similar by the SAS similarity theorem?

A
Show that the ratios the fraction with numerator cap u cap w and denominator cap z cap x and the fraction with numerator cap x cap y and denominator cap w cap v are equivalent, and angle cap w is congruent to angle cap x .
B
Show that the ratios the fraction with numerator cap u cap v and denominator cap x cap y and the fraction with numerator cap w cap v and denominator cap z cap y are equivalent, and angle cap v is congruent to angle cap y .
C
Show that the ratios the fraction with numerator cap x cap y and denominator cap v cap u and the fraction with numerator cap y cap z and denominator cap v cap w are equivalent, and angle cap u is congruent to angle cap x .
D
Show that the ratios the fraction with numerator cap x cap z and denominator cap w cap u and the fraction with numerator cap z cap y and denominator cap w cap v are equivalent, and angle cap u is congruent to angle cap z .
10

Which must be true in order for the relationship triangle ZYX approximates triangle WVU to be correct?

A
line segment ZY is parallel to line segment WV
B
angle cap z is congruent to angle cap w and angle cap x is congruent to angle cap u
C
angle cap z is congruent to angle cap y and angle cap w is congruent to angle cap v
D
line segment ZY is parallel to line segment YX and line segment WV is parallel to line segment VU
11

If the triangles are similar, which must be true?

A
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
B
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
C
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
D
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
15

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 one pair of congruent corresponding angles is sufficient to determine similar triangles
C
because angle MNL and angle ONP are congruent angles
D
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
16

triangle XYZ was reflected over a vertical line, then dilated by a scale factor of 1 half , resulting in triangle cap x prime cap y prime cap z prime Which must be true of the two triangles? Choose three correct answers.

A
triangle XYZ approximates triangle cap x prime cap y prime cap z prime
B
XZ is equal to 2X prime cap z prime
C
line segment YX is congruent to line segment cap y prime cap x prime
D
angle XZY is congruent to angle cap y prime cap z prime cap x prime
E
m angle YXZ is equal to 2 m angle cap y prime cap x prime cap z prime
18

In the diagram, m angle cap A is equal to 55 degrees and m angle cap e is equal to 35 degrees Which best explains the relationship between triangle ACB and triangle DCE ?

A
The triangles are not similar because they share a common segment and vertex.
B
The triangles are not similar because only one pair of corresponding angles is congruent.
C
The triangles are similar because all pairs of corresponding angles are congruent.
D
The triangles are similar because all right triangles can be mapped to each other using a series of transformations.
19

To prove that triangle cap l cap m cap n approximates triangle cap x cap y cap z by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

A
cap l cap m is 5 units and cap x cap z is 3 units.
B
cap l cap m is 3 units and cap x cap z is 5 units.
C
cap l cap m is 4 units and cap x cap z is 6 units.
D
cap l cap m is 6 units and cap x cap z is 4 units.

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