AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Using Triangle Congruence Theorems — Unit test Answers

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Triangle ABC is rotated 45° about point X, resulting in triangle EFD.

Question illustration
A
3.3 cm
B
3.6 cm
C
4.2 cm
D
4.5 cm
2
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Which pair of triangles can be proven congruent by the HL theorem?

A
2 right triangles have congruent hypotenuses.
Option A
B
2 triangles have one congruent angle and 2 congruent sides.
Option B
C
2 right triangles have congruent hypotenuses and another congruent side.
Option C
D
2 triangles have 3 congruent sides.
Option D
3

Consider the diagram.

Question illustration
S
SSS.
A
ASA.
S
SAS.
H
HL.
4

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.
5

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
6

Triangles A B C and E D C are shown. Triangle A B C is rotated about point C to form triangle E D C.

Question illustration
A
a rotation about point B
B
a reflection across the line containing CB
C
a reflection across the line containing AC
D
a rotation about point C
7

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Question illustration
A
A ≅ Q because of the third angle theorem.
Option A
B
AB ≅ QN because they are both opposite a right angle.
C
BC ≅ NM because it is given.
D
C ≅ M because right angles are congruent.
Option D
8

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
9

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent.

Question illustration
A
Yes, but only if AB ≅ DC.
B
Yes, but only if BC ≅ DC.
C
No, because AB is not congruent to AC.
D
No, because AB ≅ DA.
10

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
11

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

Question illustration
A
perpendicular bisector theorem
B
converse of the perpendicular bisector theorem
C
Pythagorean theorem
D
SSS congruence theorem
12

Triangle ABC is rotated 45° about point X, resulting in triangle EFD.

Question illustration
A
3.3 cm
B
3.6 cm
C
4.2 cm
D
4.5 cm
13

Triangles A B C and D E F are shown. Triangle A B C is rotated to the left about point A and then is shifted up and to the right to form triangle D E F.

Question illustration
A
Translate vertex A to vertex D, and then reflect △ABC across the line containing AC.
B
Translate vertex B to vertex D, and then rotate △ABC around point B to align the sides and angles.
C
Translate vertex B to vertex D, and then reflect △ABC across the line containing AC.
D
Translate vertex A to vertex D, and then rotate △ABC around point A to align the sides and angles.
14

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

Question illustration
A
a rotation about point A
B
a reflection across the line containing CB
C
a reflection across the line containing BA
D
a rotation about point B
15

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Question illustration
A
A ≅ Q because of the third angle theorem.
Option A
B
AB ≅ QN because they are both opposite a right angle.
C
BC ≅ NM because it is given.
D
C ≅ M because right angles are congruent.
Option D
16

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.
17

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
18

The proof that ΔRST ≅ ΔVST is shown.Given: ST is the perpendicular bisector of RV.Prove: ΔRST ≅ ΔVST

Question illustration
A
perpendicular bisector theorem
B
converse of the perpendicular bisector theorem
C
Pythagorean theorem
D
SSS congruence theorem
19

Which pair of triangles can be proven congruent by SAS?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

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

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