Prove analytically that the diagonals of a rectangle are equal

Prove that the diagonals of a rectangle are equal.

The diagonals of a rectangle are of equal length.

Prove that the diagonals of a square are equal.

The diagonals of a rectangle are of same length

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

The diagonals of a rectangle are equal and bisect each other

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.

Prove that the diagonals of a rectangle with verticles (0,0),(a,0),(a,b) and (0,b) bisect each other and are equal.

Prove that the diagonals of a rectangle ABCD with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6) are equal and bisect each other.