Question

In ∆ABC , P and Q are points on the sides AB and AC. If AP = 2cm , BP = 4cm AQ = 3cm and QC = 6cm , prove that BC = 3PQ [4 marks ]​

Answer 1

Answer:

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)

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Answer 2

Answer:

Please see the attachment