AnswersGeometrySimilarity Transformations

Similarity Transformations — Test Answers

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1
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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 angle MNL and angle ONP are congruent angles
C
because one pair of congruent corresponding angles is sufficient to determine similar triangles
D
because both triangles appear to be equilateral
3

Which describes the transformation that could have been applied to triangle ABC ?

A
An isometric transformation could have been applied because all of the vertices moved 2 units left and 2 units up.
B
A dilation could have been applied because all of the vertices decreased by 2 units.
C
An isometric transformation could have been applied because all of the vertices moved 2 units right and 2 units down.
D
A dilation could have been applied because all of the vertices increased 2 units.
4

Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

A
the fraction with numerator cap r cap s and denominator cap v cap u is equal to the fraction with numerator cap s cap t and denominator cap u cap t and angle cap s is congruent to angle cap u
B
the fraction with numerator cap r cap s and denominator cap v cap u is equal to the fraction with numerator cap t cap u and denominator cap t cap s and angle cap s is congruent to angle cap u
C
the fraction with numerator cap r cap s and denominator cap v cap u is equal to the fraction with numerator cap t cap u and denominator cap t cap s is equal to the fraction with numerator cap r cap t and denominator cap v cap t
D
the fraction with numerator cap r cap s and denominator cap v cap u is equal to the fraction with numerator cap s cap t and denominator cap u cap t is equal to the fraction with numerator cap r cap t and denominator cap v cap t
6

What is the value of y ?

A
6 square root of 3 units
B
3 square root of 3 units
C
12 square root of 3 units
D
9 square root of 3 units
7

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 f cap h cap g is 1 fourth the measure of angle cap f cap e cap d .
B
angle cap f cap h cap g is congruent to angle cap e cap f 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 d cap f cap e is congruent to angle cap g cap f cap h .
8

On a number line, the directed line segment from cap q to cap s has endpoints cap q at negative 14 and cap s at 2 Point cap r partitions the directed line segment from cap q to cap s in a ratio of 3 to 5 ratio. Which expression correctly uses the formula open paren the fraction with numerator m and denominator m plus n close paren times open paren x sub 2 minus x sub 1 close paren plus x sub 1 to find the location of point cap r ?

A
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren plus 2
B
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus negative 14 close paren plus negative 14
C
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren minus 2
D
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus 14 close paren plus 14
9

What are the coordinates of the endpoints of the segment cap t prime cap v prime ?

A
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 3 close paren
B
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 3 close paren
C
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
D
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 1 close paren
11

What is the length of line segment SR ?

A
15 units
B
18 units
C
9 units
D
12 units
13

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 translation and a dilation
B
a reflection and a dilation
C
a rotation and a reflection
D
a dilation and a rotation
14

What is the value of x ?

A
25 units
B
15 units
C
12 units
D
20 units
16

What are the coordinates of vertex cap j of the pre-image?

A
open paren 0 comma negative 4 close paren
B
open paren 0 comma negative 1 close paren
C
open paren 0 comma 4 close paren
D
open paren 0 comma 0 close paren
17

What are the coordinates of J prime ?

A
3 comma negative 5
B
1 comma negative 5
C
1 comma negative 6
D
3 comma negative 6
18

If triangle YWZ approximates triangle YXW , what is true about angle XWZ ?

A
angle XWZ is an obtuse angle.
B
angle XWZ is congruent to angle XZW .
C
angle XWZ is a right angle.
D
angle XWZ is congruent to angle WXY .
20

If the triangles are similar, which must be true?

A
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
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 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
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

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