AnswersGeometryRelationships of Triangles: Similarity and Trigonometry

Relationships of Triangles: Similarity and Trigonometry — Test Answers

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1
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In which triangle is the value of x equal to tangent inverse of open paren 3 point 1 over 5 point 2 close paren ? (Images may not be drawn to scale.)

A
Image with description A right triangle is shown. The length of 2 sides are 5 point 2 and 3 point 1. The angle opposite to side with length 3 point 1 is labeled as x.
B
Image with description A right triangle is shown. The length of the hypotenuse is 5 point 2 and the length of the side adjacent to the right angle is 3 point 1. The angle opposite to the side with length 3 point 1 is labeled as x.
C
Image with description A right triangle is shown. The length of the hypotenuse is 5 point 2 and the length of the side adjacent to the right angle is 3 point 1. The angle between the 2 sides is labeled as x.
D
Image with description A right triangle is shown. The length of the 2 sides are 5 point 2 and 3 point 1. The angle opposite to the side with length 5 point 2 is labeled as x.
2
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Which equation can be used to find the length of line segment AC ? Expand Image

A
10 times cosine times open paren 40 degrees close paren is equal to AC
B
the fraction with numerator 10 and denominator mathrm sine open paren 40 raised to the mathrm o power close paren is equal to AC
C
10 times sine times open paren 40 degrees close paren is equal to AC
D
the fraction with numerator 10 and denominator mathrm cosine open paren 40 raised to the mathrm o power close paren is equal to AC
3

What is the length of one leg of the triangle?

A
22 square root of 2 units
B
11 square root of 2 units
C
11 units
D
22 units
4

Which value of x would make line segment TV is parallel to line segment QS ?

A
11
B
10
C
8
D
3
5

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 .
6

Which equation correctly uses the value of b to solve for A ?

A
tangent of open paren 22.6 degrees close paren is equal to 12 over A
B
tangent of open paren 22.6 degrees close paren is equal to A over 13
C
tangent of open paren 22.6 degrees close paren is equal to 13 over A
D
tangent of open paren 22.6 degrees close paren is equal to A over 12
7

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
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
angle cap c is congruent to angle cap g .
8

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 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 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 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
9

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
AAS similarity theorem.
B
ASA similarity theorem.
C
SSS similarity theorem.
D
AA similarity theorem.
10

What is the length of line segment AB ? Round to the nearest tenth.

A
19 point 3 in.
B
21 point 3 in.
C
23 point 5 in.
D
68 point 0 in.
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
Yes, because corresponding sides are parallel and have lengths in the ratio 4 thirds .
C
No, because the center of dilation is not at open paren 0 comma 0 close paren .
D
No, because corresponding sides have different slopes.
12

The hypotenuse of a 45 degrees - 45 degrees - 90 degrees triangle measures 4 cm. What is the length of one leg of the triangle?

A
2 cm
B
2 square root of 2 cm
C
4 cm
D
4 square root of 2 cm
13

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 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 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 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
14

What is the scale factor of the dilation?

A
8
B
1 eighth
C
1 fourth
D
4
15

What is the value of x ?

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

What is the value of y ?

A
12 square root of 3 units
B
9 square root of 3 units
C
3 square root of 3 units
D
6 square root of 3 units
17

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 4 times greater than 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 f cap h cap g is congruent to angle cap e cap f cap d .
D
angle cap d cap f cap e is congruent to angle cap g cap f cap h .
18

Which equation can be used to find the measure of angle LJK ?

A
sine of x is equal to 15 tenths
B
cosine of x is equal to 10 over 15
C
cosine of x is equal to 15 tenths
D
sine of x is equal to 10 over 15
19

What are the angle measures of triangle VUW ?

A
m angle cap v is equal to 30 degrees , m angle cap u is equal to 60 degrees , m angle cap w is equal to 90 degrees
B
m angle cap v is equal to 30 degrees , m angle cap u is equal to 90 degrees , m angle cap w is equal to 60 degrees
C
m angle cap v is equal to 60 degrees , m angle cap u is equal to 90 degrees , m angle cap w is equal to 30 degrees
D
m angle cap v is equal to 90 degrees , m angle cap u is equal to 60 degrees , m angle cap w is equal to 30 degrees
20

What is the measure of angle LKJ ? Round to the nearest whole degree.

A
41 degrees
B
55 degrees
C
45 degrees
D
49 degrees

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