Question

Two parallel lines are intersected by a transversal at points A and B. Prove that the bisectors of the co-interior angles are perpendicular to each other.​

Answer 1

Answer

Let the angle at which the transversal intersects the lines be θ

\So, ∠BAD=θ,∠EBA=180−θ

OB bisects the ∠EBA and OA bisects the ∠BAD.

consider △AOB,∠BAO=

2

θ

∠OBA=

2

1

(180−θ)=90−

2

θ

∠BAO+∠OBA+∠BOA=180°

⟹90−

2

θ

+

2

θ

+∠AOB=180°

⟹∠AOB=90°