If each pair of opposite sides of a quadrilateral is equal, then prove that it is a parallelogram.

Given statements in a and b. Identify the statements given below as contrapositive or converse of each other. If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram (ii) If the diagonals of the quadrilateral bisect each other then it is a parallelogram.

Show that the line segments joining the midpoints of the opposite sides of a quadrilateral and bisect each other.

If the diagonals of a parallelogram are equals then show that it is a rectangle.

prove that the line segment joining the midpoints of two opposite sides of a parallelogram divides the parallelogram into two parallelograms with equal area.

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Restate the following statements with appropriate conditioins, so that they become true statements. If a quadrilateral has all its sides equal, then it is a square.

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.