AnswersAZ-Geometry A MA201Triangles and Their Side Lengths

Triangle Congruence: SAS Answers

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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
2
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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
3

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
4

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.
5

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
6

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
a
a rotation about point H
a
a reflection across the line containing HJ
a
a rotation about point K
7

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.
8

both

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

Triangles J K L and M N R are shown.

Question illustration
∠
∠J ≅ ∠M
∠
∠L ≅ ∠R
∠
∠K ≅ ∠N
∠
∠R ≅ ∠K
10

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
11

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
12

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
13

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
14

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
15

Triangles A B C and X Y Z is congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C. Triangle A B C is reflected across a line to form triangle X Y Z.

Question illustration
A
a reflection across the line containing AB
B
a reflection across the line containing AC
C
a rotation about point A
D
a rotation about point B
16

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
17

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
18

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.
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
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.
20

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

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