2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Consider triangles DAB and CBA, AD = BC [Opposite sides of a parallelogram] AB is common. AC = BD :. Ii DAB ::Ii CBA => L DAB = L CBA [Given] [ss.sJ DC A B ••.(i) [CPCT) As ABCD is a parallelogram. AD II BC and AB is transversal. .. L DAB + L CBA = 180° [Sum of interior angles on the same side of transversal is 180°.) => 2L DAB = 180° [From (i)] => L DAB = 90° As in a parallelogram, LDAB = 90°. Hence, the parallelogram is a rectangle.