Pq and rs are two lines that intersect at point t, as shown below: two lines pq and rs intersect at point t. angles ptr and stq are shown congruent. which fact is used to prove that angle ptr is always equal to angle stq? if two angles are equal to the same measure, then the angles are congruent. if two angles are equal to the same measure, then the angles are supplementary. lines pq and rs have a fixed length. lines pq and rs intersect at right angles.