Question

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

Answer 1

As, B is the midpoint of RS $\Rightarrow BR=\frac{1}{2}RS$
Also, A is the midpoint 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, PARB is a parallelogram $\Rightarrow PB||ARandAR||PB$
In $\Delta SYR$, by converse of mid point theorem X is the mid point of SY $\Rightarrow SX=XY$