Question

Question 7
Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

Answer 1

Given in $\Delta ABC$, PQ ∥ AB and PR ∥ AC and RQ ∥ BC

To show $BC=\frac{1}{2}QR$.

Proof in Quadrilateral BCAR, BR ∥CA and BC ∥ RA

So, quadrilateral , BCAR is a parallelogram.

$\therefore BC=AR$ ….(i)

Now, in quadrilateral BCQA, BC ∥AQ

And AB ∥ QC

So, quadrilateral BCQA is a parallelogram.

BC = AQ …..(ii)

On adding Eqs (i) and (ii) we get

2BC = AR + AQ

$\Rightarrow 2BC=RQ$

$\Rightarrow BC=\frac{1}{2}QR$. Hence proved