Given: l || m; ∠1 ∠3 prove: p || q horizontal and parallel lines l and m are intersected by parallel lines p and q. at the intersection of lines l and p, the uppercase left angle is angle 1. at the intersection of lines q and l, the bottom right angle is angle 2. at the intersection of lines q and m, the uppercase left angle is angle 3. complete the missing parts of the paragraph proof. we know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . we see that is congruent to by the alternate interior angles theorem. therefore, angle 1 is congruent to angle 2 by the transitive property. so, we can conclude that lines p and q are parallel by the .