Question

Prove that the bisectors of a pair of co interior angles formed by parallel lines and a transversal are perpendicular to one anotheR

Answer 1

Step-by-step explanation:

The interior angles on the same side of the transversal (called consecutive interior angles) are supplementary (they sum to 180 degrees). Call these angles a and b.

a+b=180°

=> 1/2 (a + b) = 90°

Now, let the angle formed by the bisectors be angle c.

Now there is a ∆ABC formed by the bisectors.

therefore, in the ∆ a + b + c = 180° by angle sum property

c = 90° by substitution. (hence proved)