AnswersBISD TX-Geometry A-CRTriangle Congruence: SAS

Triangle Congruence: SAS Answers

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Parallelogram V W Z X is shown. Point Y is at the bottom center of the shape. Lines are drawn from points V to X through point Y and from points W to Z through point Y. 4 triangles are formed by the lines.

Question illustration
A
Yes, along with the given information, ZX ≅ ZX by the reflexive property.
B
Yes, the triangles are both obtuse.
C
No, the sides of the triangles intersect.
D
No, there is not enough information given.
2
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How can ΔWXY be mapped to ΔMNQ?

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

both

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

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

Question illustration
A
Triangles F E G and F G L are congruent. Triangle F E G is reflected across line F G to form triangle F G L.
Option A
B
Triangles F E G and G L M are congruent. Triangle E F G is rotated about point G to form triangle G L M.
Option B
C
Triangles F E G and L M N are congruent. Triangle F E G is shifted down and to the right to form triangle L M N.
Option C
D
Triangles L M N and E F G are congruent. Triangle F E G is reflected across a line to form triangle L M N. Triangle L M N is also slightly higher and to the right of triangle E F G.
Option D
5

The proof that is shown. Select the answer that best completes the proof.Given: ΔMNQ is isosceles with base , and and bisect each other at S.Prove:

Question illustration
N
NS and QS
N
NS and RS
M
MS and RS
M
MS and QS
6

Triangles J K L and M N R are shown.

Question illustration
∠
∠J ≅ ∠M
∠
∠L ≅ ∠R
∠
∠K ≅ ∠N
∠
∠R ≅ ∠K
7

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
a
a reflection across the line containing AR
a
a reflection across the line containing AQ
a
a rotation about point R
8

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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.
10

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.
11

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
12

Triangles J K L and M N R are shown.

Question illustration
A
∠J ≅ ∠M
B
∠L ≅ ∠R
C
∠K ≅ ∠N
D
∠R ≅ ∠K
13

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
14

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
15

Triangles RQS and NTV have the following characteristics:• Right angles at ∠Q and ∠T • RQ ≅ NTCan it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not?

A
Yes, one set of corresponding sides and one corresponding angle are congruent.
B
Yes, they are both right triangles.
C
No, it is necessary to know that another set of corresponding sides is congruent.
D
No, it is not possible for the triangles to be congruent.
16

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
17

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
18

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

A
Triangles F E G and F G L are congruent. Triangle F E G is reflected across line F G to form triangle F G L.
Option A
B
Triangles F E G and G L M are congruent. Triangle E F G is rotated about point G to form triangle G L M.
Option B
C
Triangles F E G and L M N are congruent. Triangle F E G is shifted down and to the right to form triangle L M N.
Option C
D
Triangles L M N and E F G are congruent. Triangle F E G is reflected across a line to form triangle L M N. Triangle L M N is also slightly higher and to the right of triangle E F G.
Option D
19

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

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