If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel
The transversal A D intersects the two lines P Q and R S at points B and C respectively. B E is the bisector of ∠ A B Q and C F is the bisector of ∠ B C S . As, B E is the bisector of ∠ A B Q , then, ∠ A B E = 2 1 ∠ A B Q In the same way, ∠ B C F = 2 1 ∠ B C S Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom, ∠ A B E = ∠ B C F 2 1 ∠ A B Q = 2 1 ∠ B C S ∠ A B Q = ∠ B C S Therefore, by the converse of corresponding angle axiom, P Q ∥ R S .