when two parallel lines are cut transversal, which angles are not always congruent

Question

When two two parallel lines are cut transversal, which angles are not always congruent?

 

Answer 1

At each of the two points of intersection of a transversal with the parallel lines, there are four angles.

 

All of the vertical angle pairs are equal, of course; unless the transversal is perpendicular to those parallel lines, pairs of adjacent angles are merely supplementary but not equal.  

 

(Use the word congruent in lieu of the word equal, if you like--for angles, there's only one characteristic, their measurements, in degrees--so congruence of angles and equality of their measurements are really equivalent statements).