Question

$ABCD$ is a quadrilateral in which $P,Q,R$ and $S$ are mid -point of the sides $AB,BC,CD$ and $DA.AC$ is a diagonal. Show that:
(i) $SR\parallel AC$ and $SR=\frac{1}{2}AC$
(II) $PQ=SR$
(iii) $PQRS$ is a parallelogram.

Answer 1

R.E.F.Image.

In $△ABC,$ P is the mid - point

of AB and Q is the mid point

of. BC.

By mid point theorem, we have

$PQ\parallel AC$ and $PQ=\frac{1}{2}AC$ ___ (1)

${111}^{ly}$ in In ADC, R is mid pt. of CD and S is of AD

By mid point theorem

$SR\parallel AC$ and $SR=\frac{1}{2}Ac$ ___(2)

From (1) and (2) we get

$PQ\parallel SR$ and PQ = SR

we know that in a quadrilateral opposite

sides are equal and parallel then it is a

parallelogram.

$\therefore PQRS$ is a parallelogram.