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

Performance Task: Congruency Proofs — Unit test Answers

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1
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Consider the diagram.

Question illustration
A
SSS.
B
ASA.
C
SAS.
D
HL.
2
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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.
3

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
4

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
5

Which pair of triangles can be proven congruent by SAS?

A
2 triangles with identical angle measures are shown. The second triangle is shifted to the right.
Option A
B
2 triangles are shown. They have 2 congruent sides and a congruent angle. The first triangle is rotated about a point to form the second triangle.
Option B
C
2 triangles are shown. They have 1 congruent side and 2 congruent angles. The first triangle is rotated about a shared side to form the second triangle.
Option C
D
Option
Option D
6

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
8

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.
9

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
10

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
11

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
12

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.
13

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.
14

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

Question illustration
A
HL
B
SAS
C
AAS
D
SSS
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

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