Question

Solve the following problem. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it. Given two parallel lines and a transversal, at what angle do the angle bisectors of two same side interior angles intersect?

Answer 1

Answer:

Let $l_1$ and $l_2$ be two parallel lines and a third line $l_3$ is a transversal to it

A and B are the angles on the same side and the bisectors of angle A and B meet at C

We know that

When a transversal line lies on two parallel lines the sum of the internal angles on the same side of the transversal lines is 180°

Thus

∠A + ∠B = 180°

or, (1/2)(∠A + ∠B)=(1/2) × 180°

or, ∠1 + ∠2 = 90°

In triangle ABC

∠1 + ∠2 + ∠C = 180°

or, 90° + ∠C = 180°

or, ∠C = 90°

Therefore, the angle bisectors of two same side interior angles meet at right angle.

Hope this helps.