Show that the diagonals of a square are equal and bisect each other at right angles.

Show that if the diagonals of a quadrilateral are equal and bisects each other at right angles, then it is a square.

Show that if the diagonals of a quadrilateral bisects each other at right angles. Then it is a rhombus.

Show that the diagonals of a square are equal and right bisectors of each other.

Show that the diagonals of a rhombus are perpendicular to each other.

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

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 angles of an equilateral triangle are 60^@ each.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

The diagonals of a quadrilateral ABCD intersects each other at the point O such that (AO)/(BO)= (CO)/(DO) . Show that ABCD is a trapezium.