Question

Two lines are intersected by a transversal such that the bisectors of a pair of corresponding angles are equal.Prove that the lines are parallel

Answer 1

Let�l�and�m�be two lines (non-parallel) and�n�is the transversal

Given AC||BD and AB is the transversal

⇒∠1 = ∠3 ��(Since corresponding angles are equal)

⇒ 2∠1 = 2∠3 [AC is bisector of ∠A and BD is bisector of ∠B] ���

� [Since a pair of corresponding angles is equal then lines are parallel]