Given: ∠TUW ≅ ∠SRW; RS ≅ TU
Prove: ∠RST ≅ ∠UTS
Triangles R W S and U W T connect at poi...
Mathematics, 24.02.2021 23:10 kami23arap5p78v
Given: ∠TUW ≅ ∠SRW; RS ≅ TU
Prove: ∠RST ≅ ∠UTS
Triangles R W S and U W T connect at point W. A line is drawn to connect points S and T. Another line is drawn from point R to point V and down to point U. Sides S R and T U are congruent. Angles S R W and W U T are congruent.
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.
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