AnswersGeometrySimilarity Transformations

Similarity Transformations — Test Answers

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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 .
2
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What is the length of a leg of the pre-image, triangle RST ?

A
20 units
B
4 units
C
16 units
D
8 units
3

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 is equal to the fraction with numerator cap r cap t and denominator cap v cap t
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 s cap t and denominator cap u cap t and angle cap s is congruent to angle cap u
D
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
4

What is the length of line segment SR ?

A
9 units
B
18 units
C
15 units
D
12 units
5

What is the value of x ?

A
2 square root of 3 units
B
1 half square root of 3 units
C
1 third square root of 2 units
D
3 square root of 2 units
6

What is the value of y ?

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

What is the approximate value of b , rounded to the nearest tenth?

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

What is the value of x ?

A
20 units
B
12 units
C
25 units
D
15 units
9

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

A
1 half
B
10
C
1
D
0 point 1
10

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles can be mapped onto each other using dilations.
B
All equilateral triangles can be mapped onto each other using rigid transformations.
C
All equilateral triangles are congruent and therefore similar, with side lengths in a ratio of 1 to 1 ratio.
D
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
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 r cap s and denominator cap r cap y
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 x cap y and denominator cap t cap s
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 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
12

What is the length of line segment BC ?

A
9 units
B
15 units
C
11 units
D
16 units
13

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

A
angle XWZ is a right angle.
B
angle XWZ is congruent to angle XZW .
C
angle XWZ is an obtuse angle.
D
angle XWZ is congruent to angle WXY .
14

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

A
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 .
B
angle cap c is congruent to angle cap c .
C
angle cap c is congruent to angle cap g .
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 .
15

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 1 close paren
B
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
C
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 3 close paren
D
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 3 close paren
16

What is the perimeter of triangle cap A prime cap b prime cap c prime ?

A
13 cm
B
26 cm
C
52 cm
D
39 cm
17

Is triangle cap A prime cap b prime cap c prime a dilation of triangle ABC ? Explain.

A
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
B
Yes, it is an enlargement with a scale factor of 3 .
C
Yes, it is an enlargement with a scale factor of 8 thirds .
D
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
18

What is the scale factor of the dilation?

A
1 eighth
B
1 fourth
C
4
D
8
19

If CA is equal to 8 , what is cap c prime cap A prime ?

A
10 units
B
20 units
C
12 units
D
16 units
20

If PG prime equals 0 point 5 units, what is PG ?

A
3 units
B
6 units
C
2 point 5 units
D
4 point 5 units

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