Q. 14.3( 365 Votes )

ABCD is a quadril

Answer :

(i) In ΔADC, S and R are the mid-points of sides AD and CD respectively

Mid point theorem: In a triangle, the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and is half of it


SR || AC and SR = AC (1) [By mid-point theorem]


(ii) In ΔABC, P and Q are mid-points of sides AB and BC respectively. Therefore, by using mid-point theorem


PQ || AC and PQ = AC (2)


Using equations (1) and (2), we obtain


PQ || SR and PQ = SR (3)


PQ = SR


(iii) From equation (3), we obtained


PQ || SR and


PQ = SR


Clearly, one pair of opposite sides of quadrilateral PQRS is parallel and equal


Hence, PQRS is a parallelogram

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