And Are Points Sides Ab And Respectively Of В–Іabc If 2cm Pb 4cm Aq 3cms Qc 6cm Prove That Bc 3pq

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)