Question

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: $XY=QY$

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

Answer 1

The correct option is C

S1 and S2 are both true

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 $PQ\parallel RS$

Therefore, $BR=AP$ and $BR\parallel AP$

Thus, $PARB$ is a parallelogram $\Rightarrow PB\parallel AR$

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

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

Therefore, both Statement 1 and Statement 2 are true.