All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

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.

Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer.

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

The figure formed by joining the mid-points of the sides of a quadrilateral $ABCD,$ taken in order,is a square only if,

In $\Delta ABC$,the points $M$ and $N$ are on sides $AB$ and $AC$ respectively such that $AM = \frac{1}{4} AB$ and $AN = \frac{1}{4} AC$. Prove that $MN = \frac{1}{4} BC$.