Q. 95.0( 1 Vote )

# O is any point in

Answer :

Given that AB||CD and O is a point inside AB and CD.

Also, P and Q are two points on AB and CD respectively such that

OPꞱAB and OQꞱCD.

So, ∠OPA=∠OPB=90°

And ∠OQC=∠OQD=90°

Draw XY through O such that AB||XY||CD

Since, AB||XY

So, ∠YOQ=∠BPO=90° (corresponding angles)

And ∠YOP=∠DQO=90° (corresponding angles)

∴ ∠POQ=∠YOP+∠YOQ=90°+90°=180°

So, PQ is s straight line.

∴ P,O and Q are collinear.

Proved.

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