AnswersGeometry AUsing Triangle Congruence Theorems

Using Triangle Congruence Theorems — Cumulative exam Answers

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Which diagram shows possible angle measures of a triangle?

Question illustration
A
A triangle has angle lengths 35 degrees, 115 degrees, and 25 degrees.
Option A
B
A triangle has angle lengths 32 degrees, 115 degrees, and 33 degrees.
Option B
C
A triangle has angle lengths 35 degrees, 120 degrees, and 35 degrees.
Option C
D
a triangle has angle lengths 30 degrees, 120 degrees, and 20 degrees.
Option D
42
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On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, 1), (negative 4, 1) and (negative 1, 5). Triangle L M N has points (1, negative 1), (1, negative 4), and (5, negative 1).

Question illustration
A
The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
B
The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.
C
The figures are not congruent because point B corresponds with point N and point C corresponds with point M.
D
The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.
43

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 3, negative 1), (negative 1, 2), and (negative 5, 3). Triangle R S T has points (1, 1), (3, 4), and (5, 0).

Question illustration
A
ΔRST ≅ ΔACB
B
ΔRST ≅ ΔABC
C
ΔRST ≅ ΔBCA
D
ΔRST ≅ ΔBAC
44

Consider the triangle shown.

Question illustration
A
Line segment P Q, line segment R Q, line segment R P
Option A
B
Line segment R Q, Line segment P Q, line segment P Q
Option B
C
Line segment R Q, line segment R P, line segment P Q
Option C
D
Line segment R P, line segment P Q, line segment R Q
Option D
45

Point Z is the circumcenter of ΔTUV.

Question illustration
A
23.7°
B
32.8°
C
33.5°
D
57.2°
46

Which diagram has all the correct lines of reflectional symmetry for the rectangle?

A
A rectangle is folded diagonally on both corners.
Option A
B
A rectangle is folded by a vertical and horizontal line going through its center.
Option B
C
A rectangle is folded 4 ways. It is folded horizontally, vertically, and diagonally on both corners.
Option C
D
A rectangle is folded 4 ways. It is folded diagonally at each midpoint of every side.
Option D
47

On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 2, 3), (negative 2, 6), (negative 1, 6), and (negative 1, 4). Trapezoid B is reflected in quadrant 2. Trapezoid C is reflected across the y-axis. Trapezoid D is reflected into quadrant 4. Trapezoid A is reflected across the x-axis.

Question illustration
A
figure A
B
figure B
C
figure C
D
figure D
48

Which congruence theorem can be used to prove △BDA ≅ △DBC?

Question illustration
H
HL
S
SAS
A
AAS
S
SSS
49

Let p: The day is Tuesday.Let q: The day is Thursday.Let r: She comes to work.Which represents the statement "The day is Tuesday or Thursday if and only if she comes to work”?

A
p ↔ (q ∧ r)
B
p ↔ (q ∨ r)
C
(p ∧ q) ↔ r
D
(p ∨ q) ↔ r
50

On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
51

Which points lie on the line that passes through point P and is parallel to the given line? Select three options.

A
(–4, 2)
B
(–1, 3)
C
(–2, 2)
D
(4, 2)
E
(–5, –1)
52

A line contains points M, N, O, P, Q, R, S with arrows instead of endpoints.

Question illustration
A
point M
B
point N
C
point O
D
point R
53

Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.

Question illustration
A
They are complementary.
B
They are supplementary.
C
They are congruent.
D
They are obtuse.
54

How can ΔABC be mapped to ΔXYZ?

Question illustration
A
vertex B to vertex Z
B
vertex B to vertex Y
C
vertex A to vertex Z
D
vertex A to vertex Y
55

Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.

A
The rule for the translation can be written as T–3, 1(x, y).
B
The rule for the translation can be written as T–1, 3(x, y).
C
The rule for the translation can be written as(x, y) → (x + 1, y – 3).
D
The rule for the translation can be written as(x, y) → (x – 3, y + 1).
E
Trapezoid ABCD has been translated 3 units to the right and 1 unit up.
56

On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4).

Question illustration
A
rx-axis(x, y) → (–x, y)
B
ry-axis(x, y) → (–x, y)
C
rx-axis(x, y) → (x, –y)
D
ry-axis(x, y) → (x, –y)
57

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
58

The proof that UX ≅ SV is shown.Given: △STU an equilateral triangle∠TXU ≅ ∠TVSProve: UX ≅ SVWhat is the missing statement in the proof?StatementReason1. ∠TXU ≅ ∠TVS1. given2. ∠STV ≅ ∠UTX2. reflex. prop.3. △STU is an equilateral triangle3. given4. ST ≅ UT4. sides of an equilat. △ are ≅5. ?5. AAS6. UX ≅ SV6. CPCTC

Question illustration
A
△SXU ≅ △TVS
B
△UVX ≅ △SXV
C
△SWX ≅ △UWV
D
△TUX ≅ △TSV
59

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negative 2) and (0, negative 4).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
60

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.

Question illustration
A
h = 1.5
B
h = 9
C
h = 10
D
h = 13.5

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