Question

The figure shows a parallelogram PQRS, in which A is the mid point of PQ and B is the mid point of RS.
Prove that SX = XY and XY = QY.

Answer 1

As, B is the mid point of RS $\Rightarrow$ BR = $\frac{1}{2}$RS

Also, A is the mid point of PQ $\Rightarrow$ AP = $\frac{1}{2}$PQ

PQRS is a parallelogram, so that,
PQ = RS and PQ || RS

Therefore, BR = AP and BR || AP

Thus, PABR is a parallelogram $\Rightarrow$ PB || AR and AR || PB

In ΔSYR, by converse of mid point theorem X is the mid point of SY $\Rightarrow$ SX = XY

In ΔQPX, by converse of mid point theorem Y is the mid point of QX $\Rightarrow$ QY = XY