We are given that lines a and c intersect at point s. translate line a down line c until point s reaches point q. call the new line through q line b. because translations preserve orientation, lines a and b are because translations preserve angle measure, ∠rsu ≅ ∠rqu'. for the same reason, ∠rst ≅ ∠rqt', ∠psu ≅ ∠pqu', and ∠pst ≅ ∠pqt'. each of the angle pairs are corresponding angles. therefore, corresponding angles are congruent