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

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

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.

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 the diagonals of a rhombus are perpendicular to each other.

Find " If - then implications " of the following converse statements : If the diagonals of a quadrilateral bisect each other , then it is a parallelogram .

Prove that two diagonals of a parallelogram divides it into four triangles of equal areas.

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 ?

If the diagonals of a parallelogram are 3hati+hatj-2hatk and hati-3hatj+4hatk , then the area of the parallelogram is -