AnswersMathematics IISimilarity, Right Triangle Trigonometry, and Proof: Part Two

Practice Test Answers

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Which transformations could have taken place to map triangle ABC to triangle cap A double prime cap b double prime cap c double prime ?

A
a reflection and a dilation
B
a rotation and a dilation
C
a translation and a dilation
D
a reflection and a translation
2
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Which value of x would make line segment FG is parallel to line segment BC ?

A
9
B
1
C
3
D
6
3

Which statements are correct? Choose three correct answers.

A
triangle BCD is similar to triangle BSR .
B
If the ratio of BR to BD is 2 thirds , then it is possible that BS is equal to 6 and BC is equal to 3 .
C
BR over RS is equal to BS over SC
D
BR times SC is equal to RD times BS
E
BR over RD is equal to BS over SC
4

triangle XYZ was dilated, then _____________, to create triangle QAG

A
translated
B
rotated
C
reflected
D
dilated
5

Which statements are true? Choose two correct answers.

A
Side RQ corresponds to side QQ prime .
B
triangle PQR is congruent to triangle cap p prime cap q prime cap q
C
angle cap r corresponds to angle cap p prime cap q cap q prime .
D
Segment QQ prime is parallel to segment PP prime .
E
angle PQR corresponds to angle QPQ prime .
6

Point cap p partitions the directed segment from cap A to cap b into a ratio of 1 to 3 ratio. cap q partitions the directed segment from cap b to cap A into a ratio of 1 to 3 ratio. Are cap p and cap q the same point? Why or why not?

A
Yes, they both partition the segment into a ratio of 1 to 3 ratio.
B
No, cap p is 1 fourth the distance from cap A to cap b , and cap q is 1 fourth the distance from cap b to cap A .
C
No, cap q is closer to cap A and cap p is closer to cap b .
D
Yes, they are both 1 fourth the distance from one endpoint to the other.
7

What is the location of point cap g , which partitions the directed line segment from cap d to cap f into a ratio of 5 to 4 ratio? Open image in full-screen view

A
0
B
3
C
2
D
negative 1
8

Which graph shows a dilation?

A
Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 3 grid squares tall and a horizontal bottom side 6 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 1 grid square tall and a horizontal bottom side 3 grid squares long, with a slanted side connecting their endpoints.
B
Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 4 grid squares tall and a horizontal bottom side 5 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 1 grid square tall and a horizontal bottom side 2 grid squares long, with a slanted side connecting their endpoints.
C
Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 4 grid squares tall and a horizontal bottom side 5 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 2 grid squares tall and a horizontal bottom side 3 grid squares long, with a slanted side connecting their endpoints.
D
Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 3 grid squares tall and a horizontal bottom side 6 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 2 grid squares tall and a horizontal bottom side 4 grid squares long, with a slanted side connecting their endpoints.
9

A student uses the equation tangent theta is equal to the fraction with numerator s squared and denominator 49 to represent the speed, s , in feet per second, of a toy car driving around a circular track having an angle of incline theta , where sine theta is equal to 1 half To solve the problem, the student used the given value of sine theta to find the value of tangent theta and then substituted the value of tangent theta in the equation above to solve for s What is the approximate value of s , the speed of the car in feet per second?

A
9 point 2
B
5 point 3
C
28 point 3
D
7 point 5
10

An angle in standard position measures pi over 2 radians, and cap p times open paren 0 comma 1 close paren is on the terminal side of the angle. What is the value of the cosine of this angle?

A
1
B
0
C
undefined
D
negative 1
11

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

A
20 point 5 in.
B
14 point 3 in.
C
22 point 6 in.
D
21 point 3 in.
12

Which triangle is similar to triangle JKL ?

A
triangle JKM
B
triangle LJK
C
triangle KML
D
triangle MKL
13

What is the scale factor of the dilation of triangle DEF ?

A
7 thirds
B
3 tenths
C
3 sevenths
D
7
14

Given right triangle QRS , what is the value of sine of open paren 30 degrees close paren ?

A
1 half
B
the fraction with numerator square root of 3 and denominator 2
C
2 over 1
D
the fraction with numerator square root of 3 and denominator 3
15

To prove that triangle cap v cap w cap z approximates triangle cap y cap x cap z by the SAS similarity theorem, which other sides or angles should be used?

A
angle cap v cap w cap z is congruent to angle cap y cap x cap z
B
line segment cap w cap v and line segment cap x cap y
C
angle cap v cap z cap w is congruent to angle cap y cap z cap x
D
line segment cap w cap v and line segment cap z cap y
16

Given right triangle RST , what is the value of sine of cap s ?

A
12 over 13
B
5 over 13
C
13 over 12
D
5 over 12
17

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

A
3 point 0 cm.
B
12 point 8 cm.
C
10 point 5 cm.
D
9 point 8 cm.
18

What is the value of x ?

A
15 units
B
20 units
C
24 units
D
12 units
19

If RD is equal to 15 , what is RD prime ?

A
9 units
B
5 units
C
6 units
D
3 units
20

Jose also has to state that

A
angle cap A is congruent to angle cap d .
B
angle cap A is congruent to angle cap A .
C
angle cap A is congruent to angle cap A cap c cap b .
D
angle cap A is congruent to angle cap A cap b cap c .

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