Question

Given: ∠TUW ≅ ∠SRW; RS ≅ TU Prove: ∠RST ≅ ∠UTS 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.

Answer 1

I just did this problem on e2020 and its 
1.SAS
2.CPCTC

Answer 2

Answer: The paragraph proof is mentioned below.

Step-by-step explanation:

Here, Given: ∠TUW ≅ ∠SRW

And, RS ≅ TU

Where W is the intersection point of line segments TS and RU.

We have to prove that: ∠RST ≅ ∠UTS

Since, In triangles TUW and SRW

∠RWS ≅ ∠UWT ( Because they are vertical angles)

RS ≅ TU ( given)

∠TUW ≅ ∠SRW ( given)      

Then, by AAS, △TUW ≅ △SRW.

Because of CPCTC, ∠RST ≅ ∠UTS