In $\Delta ABC$,$P$,$Q$ and $R$ are the midpoints of $AB$,$BC$ and $CA$ respectively,then $\angle BAC = \angle \ldots \ldots \ldots$

In quadrilateral $ABCD$,$AC = BD$ and $AC \perp BD$. If $P, Q, R$ and $S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively,prove that $PQRS$ is a square.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $AB$,$BC$,and $CA$ respectively. If $AB = 8 \text{ cm}$,$BC = 6.6 \text{ cm}$,and $CA = 5.4 \text{ cm}$,then find the perimeter of $\Delta PQR$ in $\text{cm}$. (in $.0$)

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $PQ + BC = 8.4 \, cm$ and $AB + AC = 20.5 \, cm$,then find the perimeter of $\Delta ABC$ in $cm$.

$ABC$ is a triangle right-angled at $C$. $A$ line through the mid-point $M$ of hypotenuse $AB$ and parallel to $BC$ intersects $AC$ at $D$. Show that $MD \perp AC$.

$E$ and $F$ are respectively the mid-points of the non-parallel sides $AD$ and $BC$ of a trapezium $ABCD$. Prove that $EF \parallel AB$ and $EF = \frac{1}{2}(AB + CD)$.