Pq and rs are two lines that intersect at point t, as shown below:
(pic below)

which fact is used to prove that angle ptr is always equal to angle stq?

a) lines pq and rs have a fixed length.
b) lines pq and rs intersect at right angles.
c) if two angles are equal to the same measure, then the angles are congruent.
d) if two angles are equal to the same measure, then the angles are supplementary

Our approach to answering this question is to eliminate the choices until we are left with only one. 

(1) FALSE. The given figures are lines and can extend indefinitely.
(2) FALSE. The lines are not given to intersect in right angles. 
(3) TRUE. The angles are vertical (which means that they line in opposite side of the intersection.
(4) FALSE. The angles are not supplementary because the lines are vertical. They can only be supplementary if both are right angles.