Question

Given triangleABC, lines are drawn through A, B and C parallel respectively to the sides BC, CA and
AB forming trianglePQR. Show that BC =1/2 QR.​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer with Explanation:

In quadrilateral ABCR

AB parallel to CR and BC parallel to AR

When each pair of  opposite sides of quadrilateral are parallel then, the quadrilateral is a parallelogram.

Therefore, ABCR is a parallelogram.

BC=AR (By definition of parallelogram)..(1)

In quadrilateral AQBC

AQ is parallel to BC and AC parallel to BQ

Therefore, AQBC is a parallelogram.

BC=AQ..(2)

Adding equation (1) and equation (2)

$AR+AQ=BC+BC$

$QR=2BC$

$BC=\frac{1}{2}QR$

Hence, proved

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