Prove analytically that the diagonals of a rectangle are equal

The diagonals of a rectangle are of equal length.

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

The diagonals of a rectangle bisect each other

Diagonals of a rhombus are equal.

prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.

Prove that the diagonals of a rectangle bisect each other and are equal.

Write the negation of the following statement: Both the diagonals of a rectangle have the same length.

Prove analytically that the sum of square of the diagonals of a rectangle is equal to the sum of squares of its sides.

Using analytical geometry, prove that the diagonals of a rhombus are perpendicular to each other.