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A ABC is given. If lines are drawn through AB,B,C parallel re

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A $△ A BC$ is given. If lines are drawn through $A B, B, C$ parallel respectively to the sides $BC, C A$ and $A B$ forming $△ PQR$ , as shown in the figure, show that $BC = \frac{1}{2} QR$

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△ A BC

is given. If lines are drawn through

A B, B, C

parallel respectively to the sides

BC, C A

and

A B

forming

△ PQR

, as shown in the figure, show that

BC = \frac{1}{2} QR

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

We know that

A R ∥ BC

and

A B ∥ RC

From the figure we know that

A BCR

is a parallelogram

So we get

A R = BC

.... (1)

We know that

A Q ∥ BC

and

QB ∥ A C

From the figure we know that

A QBC

is a parallelogram

so we get

A Q = BC

.......(2)

By adding both the equations

A R + Q A = BC + BC

We know that

A R + Q A = QR

so we get

QR = 2 BC

dividing 2

BC = \frac{QR}{2}

BC = \frac{1}{2} QR

therefore it is proved that

BC = \frac{1}{2} QR

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Question Text	A $△ A BC$ is given. If lines are drawn through $A B, B, C$ parallel respectively to the sides $BC, C A$ and $A B$ forming $△ PQR$ , as shown in the figure, show that $BC = \frac{1}{2} QR$
Answer Type	Text solution:1
Upvotes	150

A △ABC is given. If lines are drawn through AB,B,C parallel respectively to the sides BC,CA and AB forming △PQR, as shown in the figure, show that BC=21​QR

Text solutionVerified

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A $△ A BC$ is given. If lines are drawn through $A B, B, C$ parallel respectively to the sides $BC, C A$ and $A B$ forming $△ PQR$ , as shown in the figure, show that $BC = \frac{1}{2} QR$