Q. 155.0( 5 Votes )

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 = 3 PQ.

Answer :


Here,


and



PQ || BC [by converse of basic proportionality theorem]


Now, take APQ and ABC


APQ = ABC (corresponding angles)


AQP = ACB (corresponding angles)


APQ ~ ABC (by AA similarity criterion)


Since, triangles are similar, hence corresponding sides will be proportional





BC = 3PQ


Hence Proved


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