If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

AC is Diameter of circle.
Hence, ∠ADC = 90° and ∠ABC = 90° …(1) [∵ Angle in a Semicircle is a right angle.]
Similarly, BD is Diameter of circle.
Hence, ∠BAD = 90° and ∠BCD = 90 …(2) [∵ Angle in a semicircle is a right angle.]
From the equation (1) and (2), ∠ADC = ∠ABC = ∠BAD = ∠BCD = 90°
Hence, ABCD is a rectangle.