Answers MISD-Geometry-RECOVERY-A-2019-2020Triangle Congruence: SSS and HL

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Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

a reflection across the line containing AB

a rotation about point B

a reflection across the line containing CB

a rotation about point C

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Which pair of triangles can be proven congruent by SAS?

2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.

2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.

2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.

2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Yes, they are congruent by either ASA or AAS.

Yes, they are both right triangles.

No, M is not congruent to NLQ.

No, there are no congruent sides.

Triangles J K L and M N R are shown.

KL ≅ NR

∠L ≅ ∠R

∠K ≅ ∠N

JK ≅ MN

The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

definition of perpendicular bisector

definition of congruence

reflexive property

substitution property

Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

dilation

reflection

rotation

translation

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

the reflexive property

ASA

AAS

the third angle theorem

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Yes, if JL ≅ XZ.

Yes, if XZ = 10.

No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

No, because the leg of one triangle is equal in length to the leg of the other triangle.

The triangles are congruent by the SSS congruence theorem.

reflection only

rotation only

translation, then reflection

translation, then rotation

Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.

No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.

No, ΔQRS and ΔABC are not congruent.

Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.

Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

LO ≅ LM

OA ≅ MA

LOA ≅ LMA

LAO ≅ LAM

Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lower and to the left of triangle L M N. Triangle H J K is reflected to form triangle L M N.

Translate K to N and reflect across the line containing HJ.

Translate K to N and reflect across the line containing JK.

Translate H to L and reflect across the line containing JK.

Translate K to L and reflect across the line containing HJ.

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.

a reflection across the line containing AB

a reflection across the line containing AC

a rotation about point A

a rotation about point B

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

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.

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.

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.

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.

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.

a reflection across the line containing HK

a rotation about point H

a reflection across the line containing HJ

a rotation about point K

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?

Yes, one set of corresponding sides and one corresponding angle are congruent.

Yes, they are both right triangles.

No, it is necessary to know that another set of corresponding sides is congruent.

No, it is not possible for the triangles to be congruent.

The triangles shown are congruent by the SSS congruence theorem.

rotation, then reflection, then translation

rotation, then translation, then reflection

translation, then reflection, then rotation

translation, then rotation, then reflection

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

Triangles Q R A and K P A are connected at point A. Triangle K P A is rotated to form triangle Q R A.

Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.

Triangles Q R A and K P L are shown. Triangle Q R A is rotated about point A and then is shifted down and to the left to form triangle K P L.

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

m∠ABC = 125° and AB ≅ DB

ΔACD is isosceles with base AD

ΔABD is isosceles with base AD

CD = 52 cm

AB = 29 cm

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

∠BAC ≅ ∠DEC

∠ACD ≅ ∠ECB

∠ACB ≅ ∠ECD

∠BCA ≅ ∠DCA

How can ΔWXY be mapped to ΔMNQ?

Option

Triangles M Z K and Q Z K share side Z K. Angles M K Z and Z K Q are congruent. Angles K Z M and K Z Q are both right angles.

a rotation about point K

a reflection across the line containing MZ

a reflection across the line containing ZK

a rotation about point Z

The triangles are congruent by SSS or HL.

translation only

reflection only

rotation, then reflection

rotation, then translation

Which shows two triangles that are congruent by AAS?

2 right triangles are connected at one side. The triangles have 1 congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle.

2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated to form the second triangle.

2 triangles are connected at one side. All sides are congruent.

2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.

The triangles are congruent by SSS or HL.

translation only

rotation only

rotation, then reflection

reflection, then translation

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