Cumulative Exam — Cumulative exam Answers

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Triangle RST has vertices R(2, 0), S(4, 0), and T(1, –3). The image of triangle RST after a rotation has verticesR'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°
22
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Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1. Which diagram illustrates these transformations?

A
Triangle A B C is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime
Option A
B
Triangle A B C is rotated about line m and then dilated to form smaller triangle A double-prime B double-prime C double-prime
Option B
C
Triangle A B C is reflected across line m and then is dilated to form larger triangle A double-prime B double-prime C double-prime
Option C
D
Triangle A B C is rotated about line m and then dilated to form larger triangle A double-prime B double-prime C double-prime
Option D
23

Triangles K L P and Q M N are shown. Triangle Q M N is slightly higher than triangle K L P and side Q M connects to side K P. Point M is at the midpoint of K P. Sides K L and Q N are congruent. Angles K L P and Q N M are congruent. Angles K P L and Q M N are both right angles.

Question illustration
A
No, KLP and QNM are congruent but KLP cannot be mapped to QNM using a series rigid transformations.
Option A
B
No, KLP and QNM are not congruent.
Option B
C
Yes, KLP can be reflected across the line containing KP and then translated so that P is mapped to M.
Option C
D
Yes, KLP can be rotated about P and then translated so that L is mapped to N.
Option D
24

Triangles C B A and R Q P are shown. The length of C B is 10, the length of B A is 10, and the length of A C is 14. The length of R Q is y, the length of Q P is 6, and the length of P R is 28.

Question illustration
A
18
B
20
C
24
D
26
25

On a coordinate plane, a line goes through (0, negative 4) and (12, 6). A point is at (12, negative 2).

Question illustration
A
y = – + 10
Option A
B
y = – + 12
Option B
C
y = – – 10
Option C
D
y = – 12
Option D
26

Point S lies between points R and T on .

Question illustration
A
2 centimeters
B
4 centimeters
C
6 centimeters
D
8 centimeters
27

Triangles A B C and E F D are shown. The lengths of sides A B and E D are congruent. Angles C A B and E D F are 33 degrees. Angle A C B is 88 degrees and angle D E F is 58 degrees.

Question illustration
A
Yes, A ≅ D and AB ≅ DE.
Option A
B
Yes, they are congruent by either AAS or ASA.
C
No, C is not congruent to any angle in DEF.
Option C
D
No, the congruent sides do not correspond.
28

Point Z is equidistant from the sides of ΔRST.

Question illustration
A
Line segment S Z is-congruent-to line segment T Z
Option A
B
Line segment R Z is-congruent-to line segment B Z
Option B
C
CTZ ASZ
Option C
D
ASZ ZSB
Option D
29

Rectangle ABCD was dilated to create rectangle A'B'C'D.

Question illustration
A
6 units
B
7.6 units
C
9.5 units
D
12 units
30

Which best explains why the orthocenter of an obtuse triangle is outside the triangle?

A
All three of the altitudes lie entirely outside the triangle.
B
Two of the altitudes lie entirely outside the triangle.
C
All three of the medians lie entirely outside the triangle.
D
Two of the medians lie entirely outside the triangle.
31

Let p: It is rainingLet q: Robert is laughing.Assume p is true. Select two statements that must logically be true.p ∨ qp ∧ qq → pp → qq ↔ p

A
p ∨ q
B
p ∧ q
C
q → p
D
p → q
E
q ↔ p
32

Which statements about the diagram are true? Select three options.

A
x = 63
B
y = 47
C
z = 117
D
x + y = 180
E
x + z = 180
33

What are the coordinates of the midpoint of EF if point E is located at (–12, 5) and point F is located at (7, –9)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
34

Triangle N L M is reflected over a line to form triangle A B C.

Question illustration
A
ΔNLM ≅ ΔCAB
B
ΔNLM ≅ ΔCBA
C
ΔNLM ≅ ΔBCA
D
ΔNLM ≅ ΔBAC
35

Planes A and B intersect.

Question illustration
A
line CD
B
line ED
C
point C
D
point D
36

On a coordinate plane, 2 triangles are shown. Triangle 1 has points at A (negative 3, 4), B (negative 2, 1), C (negative 4, 1). Triangle 2 has points at A prime (4, negative 2), B prime (3, negative 5), C prime (5, negative 5).

Question illustration
A
(x, y) → (x + 7, y + 6)
B
(x, y) → (x + 7, y – 6)
C
(x, y) → (x – 6, y + 7)
D
(x, y) → (x + 6, y + 7)
37

On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0).

Question illustration
A
3x + 5y = −9
B
3x + 5y = 9
C
5x − 3y = −15
D
5x − 3y = 15
38

Triangles R S T and V U T are connected at point T.

Question illustration
A
RT = ST
B
3ST = UT
C
∠R ≅ ∠V
D
∠V ≅ ∠U
39

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection, then rotation
B
reflection, then translation
C
rotation, then translation
D
rotation, then dilation
40

Horizontal and parallel lines c and d are cut by transversal p. At the intersection of lines c and p, the uppercase left angle is angle 1 and the uppercase right angle is angle 2. At the intersection of lines d and p, the uppercase right angle is angle 3 and the bottom left angle is angle 4.

Question illustration
A
m∠1 = 81° and m∠2 = 99°
B
m∠3 = 99° and m∠4 = 99°
C
m∠2 = 99° and m∠4 = 99°
D
m∠4 = 81° and m∠1 = 81°

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