AnswersGeometryRelationships of Triangles: Similarity

Relationships of Triangles: Similarity — Test Answers

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1
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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 translation and a dilation
B
a reflection and a dilation
C
a rotation and a reflection
D
a dilation and a rotation
2
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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 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 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
4

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

A
open paren 0 comma negative 1 close paren
B
open paren 0 comma negative 4 close paren
C
open paren 0 comma 0 close paren
D
open paren 0 comma 4 close paren
8

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 congruent to angle cap e cap f cap d .
B
angle cap d cap f cap e is congruent to angle cap g cap f cap h .
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 1 fourth the measure of angle cap f cap e cap d .
9

What is the perimeter of triangle WXY ?

A
12 point 4 6 cm
B
12 point 2 2 cm
C
14 point 5 0 cm
D
11 point 5 7 cm
10

Which statements are true? Choose three correct answers. (The formula for the area of a triangle is cap A is equal to 1 half b h )

A
AC is equal to 5 cm
B
BA is equal to 4 cm
C
The perimeter of triangle ABC is equal to 12 cm.
D
BC is equal to 6 cm
E
The area of triangle ABC is 1 third the area of triangle DEF .
11

Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?

A
Yes, because both figures are rectangles and all rectangles are similar.
B
No, because corresponding sides have different slopes.
C
Yes, because corresponding sides are parallel and have lengths in the ratio 4 thirds .
D
No, because the center of dilation is not at open paren 0 comma 0 close paren .
12

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 t cap u and denominator cap t cap s 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 s cap t and denominator cap u cap t 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
13

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

A
6 units
B
3 units
C
2 point 5 units
D
4 point 5 units
14

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
angle cap c is congruent to angle cap c .
C
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 .
D
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 .
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 3 close paren
C
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 3 close paren
D
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
18

Which statements are true? Choose three correct answers.

A
triangle DEF approximates triangle cap d prime cap e prime cap f prime
B
The distance from point cap d prime to the origin is 1 third the distance of point cap d to the origin.
C
The measure of angle cap e prime is 1 third the measure of angle cap e .
D
angle cap f corresponds to angle cap f prime .
E
Segment EE prime is parallel to segment FF prime .
19

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

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

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