Question

Q.6) If two parallel lines are intersected by a transversal, (fig.11.5)prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.
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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°

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

Step-by-step explanation:

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