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

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Solution

Given in $Δ A B C$ , PQ ∥ AB and PR ∥ AC and RQ ∥ BC

To show $B C = \frac{1}{2} Q R$ .

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

So, quadrilateral , BCAR is a parallelogram.

$∴ B C = A R$ ….(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

$\Rightarrow 2 B C = R Q$

$\Rightarrow B C = \frac{1}{2} Q R$ . Hence proved

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Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a

Δ A B C

as shown in figure. Show that

B C = \frac{1}{2} Q R

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and

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have been drawn respectively, para llel sides

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and

A B

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as shown in the figure. Show that

B C = \frac{1}{2} Q R

Through $A, B$ and $C$ lines $R Q, P R$ and $Q P$ have been drawn, respectively parallel to sides $B C, C A$ and $A B$ of a $Δ A B C$ as shown in figure. Show that $B C = \frac{1}{2} Q R$ .

A $Δ A B C$ is given. If lines are drawn through A, B, C, parallel respectively to the sides BC, CA and AB, forming $Δ P Q R$ , as shown in the adjoining figure, show that $B C = \frac{1}{2} Q R$ .