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.