AnswersTX-Geometry A IC Summer 2024-25Performance Task: Congruency Proofs

Performance Task: Congruency Proofs Answers

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

Question illustration
A
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.
B
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down.
C
The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C.
D
The figures are not congruent. Point R does not correspond with point A.
3

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
4

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
5

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.HLSASSSSASAAAS

Question illustration
A
HL
B
SAS
C
SSS
D
ASA
E
AAS
6

Given: HF || JK; HG ≅ JGProve: FHG ≅ KJG

Question illustration
A
FGH ≅ KGJ because vertical angles are congruent.
Option A
B
JKG ≅ HFG because vertical angles are congruent.
Option B
C
FHG ≅ JKG because right angles are congruent.
Option C
D
HFG ≅ KJG because alternate interior angles are congruent.
Option D
7

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
8

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
9

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
10

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
11

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.
12

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.
13

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
14

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Question illustration
A
Yes, they are congruent by SAS.
B
Yes, they are both right triangles.
C
No, the triangles share side XZ.
D
No, there is only one set of congruent sides.
15

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

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