AnswersGeometry Concepts and ConnectionsSimilarity

Similarity — Test Answers

25 verified answers3 views
1
Free Preview

What is the value of x ?

A
20 units
B
15 units
C
25 units
D
12 units
2
Free Preview

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 one pair of congruent corresponding angles is sufficient to determine similar triangles
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 both triangles appear to be equilateral
3

If the triangles are similar, which must be true?

A
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
B
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
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 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
4

What is m angle ZTB ?

A
35 degrees
B
24 degrees
C
31 degrees
D
62 degrees
5

What is the length of line segment SR ?

A
9 units
B
12 units
C
18 units
D
15 units
6

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 8 thirds .
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 3 .
D
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
7

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 reflection and a dilation
C
a translation and a dilation
D
a rotation and a reflection
8

Which must be true?

A
angle BMZ is congruent to angle CMZ
B
angle ZBM is congruent to angle ZCM
C
line segment AN is congruent to line segment LB
D
line segment NC is congruent to line segment BZ
9

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 congruent to angle cap g cap f cap h .
D
angle cap d cap f cap e is 4 times greater than angle cap g cap f cap h .
10

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
Yes, because corresponding sides are parallel and have lengths in the ratio 4 thirds .
C
No, because corresponding sides have different slopes.
D
No, because the center of dilation is not at open paren 0 comma 0 close paren .
11

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 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 1 close paren
12

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

A
12 units
B
16 units
C
10 units
D
20 units
13

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 .
14

What is the length of XB ?

A
4 point 2 cm
B
5 point 3 cm
C
4 point 8 cm
D
4 point 6 cm
15

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

A
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 .
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 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 .
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 .
16

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

A
1
B
0 point 1
C
1 half
D
10
17

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles can be mapped onto each other using 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 combinations of dilations and rigid transformations.
18

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

A
open paren 0 comma 4 close paren
B
open paren 0 comma negative 4 close paren
C
open paren 0 comma 0 close paren
D
open paren 0 comma negative 1 close paren
19

Which must be true? Choose two correct answers.

A
line segment HE is congruent to line segment HD
B
line segment LH is congruent to line segment NH
C
line segment FL is congruent to line segment FN
D
Point cap h is the center of the circle that passes through points cap l , cap m , and cap n .
E
Point cap h is the center of the circle that passes through points cap d , cap e , and cap f .
20

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

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Test

Quiz
25 verified answers

Test

Quiz
25 verified answers

Test