**P and Q are the points on the sides AB and M: respectively of a △ABC. If AP = 2cm, PB = 4cm, AQ = 3cms, Qc = 6cm, prove that BC = 3PQ.**

###### Answers:

Given: △ABC, PQ are points on AB and AC such that AP= 2 cm, BP = 4

cm,AQ= 3cm,QC=6cm

To prove: BC = 3PQ

Proof. In △ABC, AP/PB = 2/4, AQ/QC = 3/6 = 1/2

AS AP/PB = AQ/QC

According to converse of BPT, PQ || BC

In △APO and △ABC

∴ ∠APO = ∠ABC (Corresponding angles)

∠A is Common

∴△APQ ~ △ABC (AAS similarity)

∴AP/AB = AQ/QC (corresponding sides of similar △ s are proportional)

But AP/AB = PQ/BC

∴ PQ/BC = 2/6 = 1/3

∴ 3PQ = BC (Proved)