AnswersGeometry Concepts and ConnectionsSimilarity

Similarity — Test Answers

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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 angle MNL and angle ONP are congruent angles
B
because both triangles appear to be equilateral
C
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
D
because one pair of congruent corresponding angles is sufficient to determine similar triangles
2
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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
Yes, it is an enlargement with a scale factor of 8 thirds .
C
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
D
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
3

What is true about the sides of KNM ?

A
KN is equal to NM
B
KN plus NM is equal to KM
C
KM is equal to 2 times NM
D
KN is equal to 1 half KM
4

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

A
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 .
B
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 .
C
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 .
D
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 .
5

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 .
6

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

A
20 units
B
16 units
C
12 units
D
10 units
7

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

A
No, because corresponding sides have different slopes.
B
Yes, because both figures are rectangles and all rectangles are similar.
C
No, because the center of dilation is not at open paren 0 comma 0 close paren .
D
Yes, because corresponding sides are parallel and have lengths in the ratio 4 thirds .
8

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

A
open paren 0 comma 0 close paren
B
open paren 0 comma negative 4 close paren
C
open paren 0 comma negative 1 close paren
D
open paren 0 comma 4 close paren
9

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 h cap i and denominator cap b 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 .
10

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 dilation and a rotation
B
a rotation and a reflection
C
a reflection and a dilation
D
a translation and a dilation
11

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 3 units and cap x cap z is 5 units.
B
cap l cap m is 4 units and cap x cap z is 6 units.
C
cap l cap m is 6 units and cap x cap z is 4 units.
D
cap l cap m is 5 units and cap x cap z is 3 units.
12

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

A
10
B
1 half
C
1
D
0 point 1
13

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
B
All equilateral triangles can be mapped onto each other using dilations.
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 rigid transformations.
14

Triangle JKL is isosceles. The measure of angle cap j is 72 degrees and the measure of angle cap k is 36 degrees Which statement describes angle cap l ?

A
Angle cap l is a base angle and measures 72 degrees .
B
Angle cap l is a base angle and measures 36 degrees .
C
Angle cap l is a vertex angle and measures 36 degrees .
D
Angle cap l is a vertex angle and measures 72 degrees .
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 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
B
cap t prime times open paren negative 1 comma 2 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

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

A
6 units
B
4 point 5 units
C
2 point 5 units
D
3 units
17

What is the scale factor of the dilation?

A
1 fourth
B
1 eighth
C
4
D
8
18

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

A
4 units
B
8 units
C
16 units
D
20 units
19

We are given line segment AB is parallel to line segment DE Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal line segment CB and are therefore congruent, so angle CED is congruent to angle CBA We can state angle cap c is congruent to angle cap c using the reflexive property. Therefore, triangle ACB approximates triangle DCE by the

A
ASA similarity theorem.
B
SSS similarity theorem.
C
AAS similarity theorem.
D
AA similarity theorem.
20

What is m angle ZTB ?

A
24 degrees
B
62 degrees
C
31 degrees
D
35 degrees

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