Question

4. 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. bolon mirror​

Answer 1

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=

$\frac{ θ }{2}$

∠OBA=

$\frac{1}{2}$

(180−θ)=90−

$\frac{θ }{2}$

∠BAO+∠OBA+∠BOA=180°

⟹90−

$\frac{θ}{2}$

$\frac{θ}{2}$

+∠AOB=180°

⟹∠AOB=90°

∴ the bisectors of internal angles on the same side of the transversal intersects at right angles

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