Prove that if the lengths of the two diagonals of a parallelogram be equal , then the parallelogram is a rectangle.

Statement 1: If | vec a+ vec b|=| vec a- vec b| , then vec a and vec b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle. Which of the following Statements is/are correct ?

Prove that if the lengths of two diagonals of any parallelogram be equal and if the diagonals intersect each other orthogonally, then the parallelogram is a square.

Prove that if the two diagonals of any parallelogram intersect each other orthogonally, then the parallelogram is a rhombus.

Prove that if one of the angles of a parallelogram be a right -angle , then it should be a rectangle.

If diagonals of a parallelogram bisect each other, prove that its a rhombus.

Using vector method show that the diagonals of a parallelogram bisect each other.

Fill in the gaps. The diagonals of parallelogram _______ each other.

Prove that a cyclic parallelogram must be a rectangle.