Question

Prove that If two parallel lines are cut by a transversal then, any two angles are either congruent or supplementary?

Answer 1

See the proof below

Explanation:

(1) Angles `/_a` and `/_b` are supplementary by definition of supplementary angles.

(2) Angles `/_b` and `/_c` are congruent as alternate interior.

(3) From (1) and (2) `=> /_a` and `/_b` are supplementary.

(4) Angles `/_a` and `/_d` are congruent as alternate interior.

(5) Considering any other angle in this group of 8 angles formed by two parallel and transversal, we (a) use the fact that it is vertical and, consequently, congruent to one of the angles analyzed above and (b) use the property of being congruent or supplemental proved above.