Question

Prove that the line segment joining the midpoints of the adjacent side of the quadrilateral

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

$\blue{\boxed{\sf Given}}$

A quadrilateral ABCD in which P. Q, R and S are the mid-points of sides AB, BC, CD and DA respectively.

$\blue{\boxed{\sf To/: prove }}$ PQRS is a

parallelogram

CONSTRUCTION Join AC.

PROOF In A ABC, P and Q are the mid-points of AB and BC respectively.

PQ || AC

In Δ ACD, R and S are the mid-points of CD and DA

respectively.

SR || AC

From equations (i) and (ii), we have

PQ II AC and SR || AC

PQ || SR.

Similarly, by considering triangles ABD and BCD, we can prove that

PS || QR.

Hence proved