Through A,B and C lines RQ,PR and QP have been drawn, respectively parallel to sides BC,CA and AB of a ΔABC as shown in figure. Show that BC=12QR.
Given in ΔABC, PQ∥AB and PR∥AC and RQ∥BC
To show BC=12QR.
Proof: In Quadrilateral BCAR,BR∥CA and BC∥RA
So, quadrilateral , BCAR is a parallelogram.
Now, in quadrilateral BCQA,BC∥AQ and AB∥QC
So, quadrilateral BCQA is a parallelogram.
On adding Eqs (i) and (ii) we get