AnswersCR CCSS Math 2 S2 M2960OXSolving for Angle Measures of Right Triangles

Solving for Angle Measures of Right Triangles — Unit test Answers

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1
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In the diagram, .

Question illustration
A
WV and XY
B
WV and ZY
C
∠VZW ≅ ∠YZX
D
∠VWZ ≅ ∠YXZ
2
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The hypotenuse of a 45°-45°-90° triangle measures units.

Question illustration
A
7 units
B
units
Option B
C
14 units
D
units
Option D
3

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

Question illustration
A
16.7°
B
17.5°
C
72.5°
D
73.3°
4

Quadrilateral FGHJ is dilated according to the ruleDO,(x,y) to create the image quadrilateral F'G'H'J', which is not shown.

Question illustration
A
(-2,-4)
B
(-2,-6)
C
(Negative nine-halves, negative 4)
Option C
D
(Negative nine-halves, negative 9)
Option D
5

Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot

Question illustration
A
m∠A = 30°, m∠B = 60°, m∠C = 90°
B
m∠A = 90°, m∠B = 60°, m∠C = 30°
C
m∠A = 60°, m∠B = 90°, m∠C = 30°
D
m∠A = 90°, m∠B = 30°, m∠C = 60°
6

Triangle MRN is created when an equilateral triangle is folded in half.

Question illustration
A
units
Option A
B
4 units
C
units
Option C
D
8 units
7

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C.

Question illustration
A
a reflection and a dilation
B
a rotation and a dilation
C
a translation and a dilation
D
a reflection and a translation
8

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle.

Question illustration
A
ΔJKM
B
ΔMKL
C
ΔKML
D
ΔLJK
9

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Question illustration
A
cos−1 = x
Option A
B
cos−1 = x
Option B
C
sin−1 = x
Option C
D
sin−1 = x
Option D
10

Two similar triangles are shown.

Question illustration
A
translated
B
reflected
C
dilated
D
rotated
11

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

A
33.6°
B
39.8°
C
50.2°
D
56.4°
12

Read the proof.Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°Prove: △HKJ ~ △LNP

Question illustration
A
CPCTC
B
definition of supplementary angles
C
triangle parts relationship theorem
D
triangle angle sum theorem
13

Which best explains whether or not all isosceles triangles are similar?

A
All isosceles triangles are similar. Two angles within each triangle are always congruent.
B
All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.
C
All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
D
All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.
14

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

Question illustration
A
60 ft
B
ft
Option B
C
120 ft
D
ft
Option D
15

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Question illustration
A
27.7°
B
31.7°
C
58.3°
D
62.3°
16

The hypotenuse of a 45°-45°-90° triangle measures in.

Question illustration
A
5 StartRoot 5 EndRoot
Option A
B
5 StartRoot 10 EndRoot
Option B
C
10 StartRoot 5 EndRoot
Option C
D
10 StartRoot 10 EndRoot
Option D
17

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B.

Question illustration
A
183 meters
B
250 meters
C
366 meters
D
683 meters
18

Line segment JL is an altitude in triangle JKM.

Question illustration
A
JKM is a right triangle because KL + LM = 15.3.
B
JKM is a right triangle because KL + LM = 18.2.
C
JKM is not a right triangle because KL + LM ≠ 15.3.
D
JKM is not a right triangle because KL + LM ≠ 18.2.
19

Which statements are correct? Select three options.

A
△BCD is similar to △BSR.
B
StartFraction B R Over R D EndFraction = StartFraction B S Over S C EndFraction
Option B
C
If the ratio of BR to BD is , then it is possible that BS = 6 and BC = 3.
Option C
D
(BR)(SC) = (RD)(BS)
E
StartFraction B R Over R S EndFraction = StartFraction B S Over S C EndFraction
Option E
20

To prove that ΔAED ˜ ΔACB by SAS, Jose shows that .

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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