1
Using Triangle Congruence Theorems
Questions with Correct Answers for a Specific
Exam Mail
Which congruency theorem can be used to prove that △ABD ≅ △DCA?
Ans: C. SAS
In the figure below, WU ≅ VT. The congruency theorem can be used to prove
that △WUT ≅ △VTU.
Ans: B. HL
Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
Ans: B. ASA
Analyze the diagram below. Which statements regarding the diagram are
correct? Check all that apply.
Ans: 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.
Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her
proof?
Ans: A. ΔACD ≅ ΔECB
Complete the paragraph proof.
Pretest - Stuvia US
, 2
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.
Ans: 1. SAS
2. AD
Mikal is proving that AE ≅ CE . Which reason does the ♣ represent in Mikal's
proof?
Ans: D. AAS
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.
Ans: 1.SAS
2.CPCTC
Pretest - Stuvia US
Using Triangle Congruence Theorems
Questions with Correct Answers for a Specific
Exam Mail
Which congruency theorem can be used to prove that △ABD ≅ △DCA?
Ans: C. SAS
In the figure below, WU ≅ VT. The congruency theorem can be used to prove
that △WUT ≅ △VTU.
Ans: B. HL
Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
Ans: B. ASA
Analyze the diagram below. Which statements regarding the diagram are
correct? Check all that apply.
Ans: 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.
Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her
proof?
Ans: A. ΔACD ≅ ΔECB
Complete the paragraph proof.
Pretest - Stuvia US
, 2
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.
Ans: 1. SAS
2. AD
Mikal is proving that AE ≅ CE . Which reason does the ♣ represent in Mikal's
proof?
Ans: D. AAS
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.
Ans: 1.SAS
2.CPCTC
Pretest - Stuvia US
