Given ∆ABC, lines are drawn through A, B, and C, parallel respectively to the sides BC, CA and AB, forming ∆PQR. Then, which of the following is correct.

BC=

\frac{3}{2}

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BC=

\frac{1}{2}

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BC=

\frac{1}{4}

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BC=

\frac{5}{2}

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Solution

The correct option is B BC= $\frac{1}{2}$ QR
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)

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