In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

$ABCD$ is a parallelogram and $P$ and $Q$ are points on the diagonal $AC$ such that $AP = PQ = QC$. Prove that $BQ \parallel DP$ and $BD$ bisects $PQ$.

Prove that the diagonals of a square are equal and bisect each other at right angles.

$D, E$ 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 trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 80^{\circ}$ and $\angle B = 75^{\circ}$,then find $\angle D$. (in $^{\circ}$)

Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.