Question

The figure shows a parallelogram PQRS in which A is the mid point of PQ and B is the mid point of RS.

S1 : SX = XY

S2 : XY = QY

• A. S1 is true but S2 is false
• B. S1 is false but S2 is true
• C. S1 and S2 are true
• D. S1 and S2 are false

Answer 1

The correct option is C

S1 and S2 are true

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

A is 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

Therefore BR = PQ and PABR is a parallelogram $\Rightarrow$ PA || BR 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

Therefore both S1 and S2 are true.