If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

Statement 1 : If |veca + vecb| = |veca - vecb| , then veca and vecb are perpendicular to each other. Statement 2 : If the diagonals of a parallelogram are equal in magnitude, then the parallelogram 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.

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 ?

The diagonals of a rectangle are of equal length.

If the two diagonals of a parallelogram are equal, it is a rectangle.

The opposite angles of a parallelogram are equal.

The diagonals of a parallelogram bisect each other.

Prove that any cyclic parallelogram is a rectangle.

Prove that any cyclic parallelogram is a rectangle.

If the sides of a parallelogram touch a circle prove that the parallelogram is a rhombus.