Question

prove that the figures formed by joining the mid-point of the adjacent side of a quadrilateral is a parallelogram

Answer 1

HEY THERE !!

THE PROOF OF UR QUESTION IS GIVEN BELOW

Let ABCD a quadrilateral and P,Q,R,S are the mid points of sides AB,BC,CD,DA respectively.

Join AC and be it a diagonal

In triangle ADC , S is the mid point of DC.

Therefore,
SR||AC and SR=1/2 AC ........(1)
( by mid point theorem)

In triangle ABC , P is mid point of AB nad Q is mid point of BC.

Therefore,
PQ||AC and PQ=1/2 AC .......(2)
(by mid point theorem)


FROM EQUATION (1) AND (2),

SR||PQ and SR = PQ.

THEREFORE,
In quadrilateral PQRS, one pair of opposite sides is equal and parallel.
Therefore,
PQRS is a parallelogram.

Hence, proved


THANk YOU
@srk