Using Triangle Congruence Theorems Answers

1

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Mikal is proving that AE ≅ CE . Which reason does the ♣ represent in Mikal’s proof?

A

SAS

B

SSS

C

ASA

D

AAS

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Complete the paragraph proof.

Answers:

We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then deter:SAS

We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then deter:AD

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BA✔ AD AE BE

A

BA

B

✔ AD

C

AE

D

BE

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Complete the paragraph proof:

Answers:

It is given that ∠TUW ≅ ∠SRW and RS ≅ TU. Because ∠RWS and ∠UWT are vertical angles and vertical angles are congruent, ∠RWS ≅ ∠UWT. Then, by AAS, △TUW ≅ △SRW. Because CPCTC, SW ≅ TW and WU ≅ RW. Becau:SAS

It is given that ∠TUW ≅ ∠SRW and RS ≅ TU. Because ∠RWS and ∠UWT are vertical angles and vertical angles are congruent, ∠RWS ≅ ∠UWT. Then, by AAS, △TUW ≅ △SRW. Because CPCTC, SW ≅ TW and WU ≅ RW. Becau:CPCTC

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SAS ASA AAS✔ CPCTC

A

SAS

B

ASA

C

AAS

D

✔ CPCTC

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Analyze the figure and the two-column proof.

Answers:

♣: Δ ≅ ΔAFC ♦::DEB

♣: Δ ≅ ΔAFC ♦::HL

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ASA AAS✔ HL SAS

A

ASA

B

AAS

C

✔ HL

D

SAS

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