State whether the following statement is true or false:
The diagonals of a rhombus bisect each other at right angles.

In $\Delta PQR$,$X, Y$ and $Z$ are the midpoints of $PQ, QR$ and $RP$ respectively. If $PQ = 7.2 \, cm$,$PR = 8.4 \, cm$ and $XZ = 3.8 \, cm$,then find the perimeter of $\Delta PQR$ and $\Delta XYZ$.

In $\Delta XYZ$,$A$ and $B$ are the midpoints of $XY$ and $XZ$ respectively. If $AB = 7.5 \, cm$,then find the length of $YZ$ in $cm$.

In trapezium $ABCD$,$AB || CD$. Points $P$ and $Q$ are the midpoints of $AD$ and $BC$ respectively. If $AB = 18 \, cm$ and $PQ = 15 \, cm$,then $CD = \dots \, cm$.

State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

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.