$(1)$ $A$ quadrilateral in which only one pair of opposite sides are parallel is a $\ldots \ldots \ldots$.
$(2)$ The diagonals of a rectangle are $\ldots \ldots \ldots$.

Diagonals of a parallelogram $ABCD$ intersect at $O.$ If $\angle BOC = 90^{\circ}$ and $\angle BDC = 50^{\circ},$ then $\angle OAB$ is (in $^{\circ}$)

$PQ$ and $RS$ are two equal and parallel line segments. Any point $M$ not lying on $PQ$ or $RS$ is joined to $Q$ and $S$. Lines are drawn through $P$ parallel to $QM$ and through $R$ parallel to $SM$,meeting at $N$. Prove that line segments $MN$ and $PQ$ are equal and parallel to each other.

$(1)$ The diagonals of a rhombus are ....... to each other.
$(2)$ The diagonals of a parallelogram ...... each other.

In a quadrilateral $ABCD$,$\angle A : \angle B : \angle C : \angle D = 4 : 5 : 4 : 5$. Find the measure of each angle of the quadrilateral and state the type of quadrilateral $ABCD$.

$D, E$ 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.