Using Triangle Congruence Theorems

Question 1

Which congruency theorem can be used to prove that △ABD ≅ △DCA?

Revolt · Accepted Answer

SAS

Question 2

BA✔ AD AE BE

Revolt · Accepted Answer

✔ AD

Question 3

Which congruency theorem can be used to prove that △GHL ≅ △KHJ?

Revolt · Accepted Answer

ASA

Question 4

Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof? Triangles A C D and E C B are shown. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C B. Angles C A D and B E C are congruent. The lengths of line segments A B and D E are congruent. The lengths of line segments B C and C D are congruent.

Revolt · Accepted Answer

ΔACD ≅ ΔECB

Question 5

ASA✔ SAS AAS SSS

Revolt · Accepted Answer

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: 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

Question 6

Mikal is proving that AE ≅ CE . Triangles A B E and C D E are connected at point E. Angles A B E and E D C are right angles. The lengths of A C and D C are congruent. Which reason does the ♣ represent in Mikal’s proof?

Revolt · Accepted Answer

AAS

Question 7

SASASA AAS CPCTC

Revolt · Accepted Answer

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: 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

Question 8

Analyze the figure and the two-column proof.

Revolt · Accepted Answer

✔ DEB; ♣: Δ ≅ ΔAFC ♦:: DEB; ♣: Δ ≅ ΔAFC ♦:: HL

Question 9

SAS ASA AAS✔ CPCTC

Revolt · Accepted Answer

✔ CPCTC

Question 10

ASA AAS✔ HL SAS

Revolt · Accepted Answer

✔ HL

Using Triangle Congruence Theorems Answers

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