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Question

P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2 cm, PB = 4 cm, AQ = 3 cm, and QC = 6 cm, show that BC = 3PQ.


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Solution


AP/PB = AQ/QC
2/4 =3/6
1/2 = 1/2

Therefore, PQ || BC [Converse of basic proportionality theorem.]

ΔAPQ ~ ΔABC

AP/AB = AQ/AC = PQ/BC

2/6 = 3/9 = PQ/BC

PQ/BC = 1/3

BC = 3 PQ.

Hence proved


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