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


OPAB and OQCD.


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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