Question

$ABCD$ is a quadrilateral in which $P,Q,R$ and $S$ are mid-points of the sides $AB,BC,CD$ and $DA$ respectively. Show that $PQRS$ is a parallelogram.

Answer 1

Construction: Join AC

Proof:

In $△ADC$

P and Q are mid points

$\therefore PQ\parallel AC$...(1)

In $△ABC$

R and S are mid points

$\therefore SR\parallel AC$...(2)

From (1) and (2) we get,

$\therefore PQ\parallel SR$

Simillarly

$\therefore PS\parallel QR$

Hence proved, that PQRS is a parallelogram.