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

Statement 1: If | vec a+ vec b|=| vec a- vec b|,t h e n vec aa n d vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Area of a parallelogram =_____

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

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

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

Prove that each diagonal of a parallelogram divides it into two congruent triangles.

The diagonals of a parallelogram are expressed as vecA=5hati05hatj+3hatk and hatB=3hatj-2hatj-hatk . Calculate the magnitude of area of this parallelogram.