Using Triangle Congruence Theorems

Question 1

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

Revolt · Accepted Answer

C: SAS

Question 2

Question 2

Revolt · Accepted Answer

B: HL

Question 3

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

Revolt · Accepted Answer

B: ASA

Question 4

Which statements regarding the diagram are correct? Check all that apply.

Revolt · Accepted Answer

A: ST ≅ ST by the reflexive property.; B: ∠RWS ≅ ∠UWT because they are vertical angles.; C: △RWS ≅ △UWT by AAS.; E: ∠WTU ≅ ∠WSR because CPCTC.

Question 5

Complete the paragraph proof. 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 determine △ABC ≅ △AED by . Because of CPCTC, segment AC is congruent to segment . Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.

Revolt · Accepted Answer

B: SAS

Question 6

Complete the paragraph proof: 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. Because of the definition of congruence, SW = TW and WU = RW. If we add those equations together, SW + WU = TW + RW. Because of segment addition, SW + WU = SU and TW + RW = TR. Then by substitution, SU = TR. If segments are equal, then they are congruent, so SU ≅ TR. Because of , △TRS ≅ △SUT, and because of , ∠RST ≅ ∠UTS.

Revolt · Accepted Answer

A: SAS

Question 7

Question 7

Revolt · Accepted Answer

B: AD

Question 8

Question 8

Revolt · Accepted Answer

D: CPCTC

Using Triangle Congruence Theorems Answers

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