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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