In the given Fig, two triangles ABC and DBC lie on the same side of base BC. P is a point on BC such that PQ || BA and PR || BD. Prove that: QR || AD.

increment ABC comma space

space PQ parallel to AB

By BPT theorem

CP over BP equals CQ over AQ

...(i)

Now in

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PR parallel to BD

rightwards double arrow

By using BPT

CP over BP equals CR over RD

...(ii)

From (i) and (ii)

space CP over BP equals CP over BP

rightwards double arrow

By converse of BPT,

QR parallel to AD.

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