In $\Delta ABC$,$X$ and $Y$ are the midpoints of $AB$ and $AC$ respectively. State the type of quadrilateral $XBCY$.

Can the angles $110^{\circ}, 80^{\circ}, 70^{\circ}$ and $95^{\circ}$ be the angles of a quadrilateral? Why or why not?

$ABCD$ is a trapezium such that $AB || CD$. If $\angle A = y + 60^{\circ}$,$\angle B = x + 60^{\circ}$,$\angle C = 3x - 40^{\circ}$ and $\angle D = 3y - 80^{\circ}$,then find the measure of each angle of $ABCD$.

Perimeter of rectangle $PQRS$ is $40\, cm$. If $PQ : QR = 3 : 5$,then $RS = \ldots \ldots \ldots \, cm$.

$D, E$ and $F$ are respectively the mid-points of the sides $AB, BC$ and $CA$ of a triangle $ABC$. Prove that by joining these mid-points $D, E$ and $F$,the triangle $ABC$ is divided into four congruent triangles.

In parallelogram $PQRS$,the bisector of $\angle P$ intersects $RS$ at $M$ and the bisector of $\angle R$ intersects $PQ$ at $N$. Prove that $PNRM$ is a parallelogram.