SAS, ASA, AAS

SAS, ASA, AAS

by David Miller

​Lesson Informaiton

​Standards...MGSE9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of

congruence in terms of rigid motions. (Extend to include HL and AAS.)

​

​

​Essential Question:

-What information would you use to prioritize triangle congruence? 

-How would you portray two congruent triangles?

​Congruent angles & segments follow the same order in the other triangle

Multiple Choice

What does the word CONGRUENT mean? 

• Cranky
• Different
• The Same
• Crazy 

Multiple Choice

∆ABC≅∆XYZ
which is true?

• AB≅XY
• AB≅YX
• AB≅XZ
• BC≅CB

Multiple Choice

Use the congruency statement to answer the following: 
<F = ___

• <H
• <I
• <G
• not congruent to another angle

Multiple Choice

Complete the congruence statement:

$$\Delta WXY\cong\Delta$$  

• ZAY

• YZA

• ZYA

• AZY

Multiple Choice

Complete the congruence statement.

• CRP
• PCR
• RPC
• PRC

​Notice how the features occur IN THAT ORDER

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS
• ASA
• AAS
• SAS

​​ASA...notice how the features occur IN THAT ORDER

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• SAS
• HL
• ASA

​Notice how they do not occur in order. The side length is not included

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• ASA
• SSA
• AAA

​Proves that SIDES of triangles are congruent

Multiple Choice

What shortcut would you use to prove the triangles congruent?

• SSS
• SAS
• ASA
• AAS

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by AAS

• Yes - by ASA

• Yes - by HL

• Yes - by SAS

• Not congruent

Multiple Choice

How are these two triangles congruent?

• AAS
• ASA
• Not enough information
• SAS

Multiple Choice

How are these triangles congruent?

• AAS
• ASA
• SAS
• Not enough information

Multiple Choice

To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?

• ∠DEF ≅ ∠ DGF

• ∠DFE ≅ ∠ DFG

• DE ≅ DG

• DG ≅ GF

​M is the midpoint of RS. M is the midpoint of PQ. Prove that the triangles are congruent

​Start with what is given

​

​What is needed to prove congruence?

​

​These shapes have vertical angles, which prove SAS

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SAS
• ASA
• AAS
• Not enough information

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by SAS

• Not congruent

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• HL

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by AAS

• Not congruent

Multiple Choice

Which shows two triangles that are congruent by ASA?

Multiple Choice

State if the triangles are congruent or not. If they are, state how you know.

• Yes - by SSS

• Yes - by ASA

• Yes - by HL

• Yes - by SAS

• Not congruent

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• ASA
• AAS
• SAS
• AAA

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS
• SSA
• ASA
• AAS

Multiple Choice

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• AAA
• AAS
• ASA
• Not necessarily congruent

Multiple Choice

Can ΔTSR and ΔQRS be proven congruent by SAS?

• yes, because along with the given information on the diagram,  SR ≅ RS by the reflexive property

• yes, because a reflection will map ΔTSR onto ΔQRS

• yes, because P appears to be the midpoint of SQ and TR

• no, because not enough is information given to prove the triangles congruent by SAS

Multiple Choice

In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?

• ∠J ≅ ∠M

• ∠L ≅ ∠R

• ∠K ≅ ∠N

• ∠R ≅ ∠K

Multiple Choice

Can you conclude that triangle GHF is congruent to triangle GJK? Explain

• yes, by ASA 

• yes, by AAS

• yes, by SAS

• Not enough Information Given

Multiple Choice

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• SSA
• AAS
• ASA
• Not necessarily congruent

Multiple Choice

Are the triangles congruent? If so, how do you know?

• yes, because all the angles of the triangles are acute

• yes, because the triangles have three congruent, corresponding angles

• yes, because of ASA or AAS

• not enough information given

Multiple Select

What additional information could be used to PROVE that the triangles are congruent using AAS? Select two options

• C ≅ Q

• CB ≅ QM

• AC = 3.9cm and RQ = 3.9cm

• mC = 35° and mQ = 35°

• AB = 2.5cm and MQ = 2.5cm

Multiple Select

Which statements are true about additional information for proving that the triangles are congruent? Select two options.

• If A ≅ T, then the triangles would be congruent by ASA. 

• If B ≅ P, then the triangles would be congruent by AAS. 

• If all the angles are acute, then the triangles would be congruent. 

• If C and Q are right angles, then triangles would be congruent. 

• If BC ≅ PQ, then the triangles would be congruent by ASA.