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

Prove that the line segment joining the mid-points of the non-parallel sides of a trapezium is parallel to the parallel sides of the trapezium.

In a parallelogram $ABCD$,$\angle A = 5x - 40^{\circ}$ and $\angle C = 3x + 10^{\circ}$,then $x = \ldots$

Two parallel lines are intersected by a transversal. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

$A$ diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

In $\Delta XYZ$,$A, B$ and $C$ are the midpoints of $XY, YZ$ and $XZ$ respectively. If $AB = 5.2\, cm$,$BC = 4.3\, cm$ and $AC = 6.5\, cm$,then find the perimeter of $\Delta XYZ$ in $cm$.