AnswersGCSS_GA-Geometry Concepts and Connections_ICUnit Test

Triangle Congruence: SAS Answers

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Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.

Question illustration
A
Translate H to L and rotate about H until HK lies on the line containing LM.
B
Translate K to M and rotate about K until HK lies on the line containing LM.
C
Translate K to N and rotate about K until HK lies on the line containing LN.
D
Translate H to N and rotate about H until HK lies on the line containing LN.
2
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The proof that ΔEFG ≅ ΔJHG is shown.Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.Prove: ΔEFG ≅ ΔJHG Statement Reason1.G is the midpoint of HF1.given2.FG ≅ HG2.def. of midpoint3.EF ∥ HJ3.given4.?4.alt. int. angles are congruent5.EF ≅ HJ5. given6.ΔEFG ≅ ΔJHG6.SAS

Question illustration
A
∠FEG ≅ ∠HJG
B
∠GFE ≅ ∠GHJ
C
∠EGF ≅ ∠JGH
D
∠GEF ≅ ∠JHG
3

Triangles J K L and M N R are shown.

Question illustration
A
∠J ≅ ∠M
B
∠L ≅ ∠R
C
∠K ≅ ∠N
D
∠R ≅ ∠K
4

Which of these triangle pairs can be mapped to each other using a single translation?

A
Triangles C E D and C N P are congruent. Triangle C E D is rotated about point C and then reflected across a line to form triangle C N P.
Option A
B
Triangles C N E and C E D are congruent. Triangle C N E is reflected across a line and then rotated slightly to form triangle C E D.
Option B
C
Triangles C E D and M D P are congruent. Triangle M D P is rotated and shifted up to form triangle C E D.
Option C
D
Triangles C E D and M P N are congruent. Triangle C E D is shifted to the right to form triangle M P N.
Option D
5

Which of these triangle pairs can be mapped to each other using both a translation and a rotation about C?

A
Triangles X Y C and A B C are shown. Both triangles are congruent and share common point C. Triangle A B C is slightly lower than triangle X Y C.
Option A
B
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is identical to triangle A B C but is slightly higher.
Option B
C
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is reflected across a line to form triangle A B C.
Option C
D
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is rotated down and to the left to form triangle A B C. It is also slightly higher than triangle A B C.
Option D
6

If bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three options.

Question illustration
A
m∠ABC = 125° and AB ≅ DB
B
ΔACD is isosceles with base AD
C
ΔABD is isosceles with base AD
D
CD = 52 cm
E
AB = 29 cm
7

The proof that ΔACB ≅ ΔECD is shown.Given: AE and DB bisect each other at C.Prove: ΔACB ≅ ΔECD

Question illustration
A
∠BAC ≅ ∠DEC
B
∠ACD ≅ ∠ECB
C
∠ACB ≅ ∠ECD
D
∠BCA ≅ ∠DCA
8

Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.

Question illustration
A
a reflection across the line containing HK
B
a rotation about point H
C
a reflection across the line containing HJ
D
a rotation about point K
9

Triangles A Q R and A K P share point A. Triangle A Q R is rotated up and to the right for form triangle A Q R.

Question illustration
A
a rotation about point A
B
a reflection across the line containing AR
C
a reflection across the line containing AQ
D
a rotation about point R
10

How can ΔWXY be mapped to ΔMNQ?

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

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