Q. 105.0( 2 Votes )

The figure formed A. Parallelogram

B. Rectangle

C. Square

D. Rhombus

Answer :

Given that,

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


To prove: PQRS is a parallelogram


Construction: Join A with C


Proof: In ,


P and Q are the mid-points of AB and BC respectively


Therefore,


PQ AC and PQ = AC (Mid-point theorem) (i)


Again,


In ,


R and S are mid-points of sides CD and AD respectively


Therefore,


SR AC and SR = AC (Mid-point theorem) (ii)


From (i) and (ii), we get


PQ SR and PQ = SR


Hence, PQRS is a parallelogram (One pair of opposite sides is parallel and equal)

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