In a parallelogram, the diagonals intersect each other at right angles.

State whether the given sentence is true or false:

In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

If all the angles of a quadrilateral are equal, it is a parallelogram.

If three sides of a quadrilateral are equal, it is a parallelogram.

If three angles of a quadrilateral are equal, it is a parallelogram.

If all the sides of a quadrilateral are equal, it is a parallelogram.

In figure, $ABCD$ is a parallelogram in which $\angle A=60°$. If the bisectors of $\angle A$ and $\angle B$ meet at $P$, prove that $AD=DP, PC=BC$ and $DC=2AD$.

In the given figure, $ABCD$ is a parallelogram and $E$ is the midpoint of side $BC.$ If $DE$ and $AB$ when produced meet at $F$, prove that $AF=2AB.$