In the given figure, $ABCD$ is a rhombus. Then 

In a trapezium $ABCD$, if $AB\Vert CD$, then $\left(A{C}^2+B{D}^2\right)=?$

In the given figure, $AD$ is a median of $∆ABC$ and $E$ is the midpoint of $AD.$ If $BE$ is joined and produced to meet $AC$ in $F$, then $AF=\frac{AC}{x}$. Find the value of $x$.

Three statements are given below:
I. In a $\Vert \mathrm{gm}$, the angle bisectors of two adjacent angles enclose a right angle.
II. The angle bisectors of a $llgm$ form a rectangle.
III. The triangle formed by joining the midpoints of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which is true?

Three statements are given below:

I. In a Rectangle $ABCD$, the diagonal $AC$ bisects $\angle A$ as well as $\angle C$.

II. In a Square $ABCD$, the diagonal $AC$ bisects $\angle A$ as well as $\angle C$.

III. In a Rhombus $ABCD$, the diagonal $AC$ bisects $\angle A$ as well as $\angle C$

Which is true?