We are given that lines a and c intersect at point s. translate line a down line c until period 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, angle a rsu is congruent to angle rqr. for the same reason, angle rsu is congruent to angle rqt, angle psu is congruent to angle pqr, and angle pst is congruent to angle pqt. each of the angle pairs are corresponding angles. therefore, corresponding angles are congruent.