The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS.
Statement 1: SX=XY
Statement 2: XY=QY
S1 and S2 are both true
As, B is the mid point of RS⇒BR=12RS
Also, A is the mid point of PQ⇒AP=12PQ
PQRS is a parallelogram, so that,
PQ=RS and PQ∥RS
Therefore, BR=AP and BR∥AP
Thus, PARB is a parallelogram ⇒PB∥AR
In △SYR, by converse of mid point theorem X is the mid point of SY⇒SX=XY
In △QPX, by converse of mid point theorem Y is the mid point of QX⇒QY=XY
Therefore, both Statement 1 and Statement 2 are true.