2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Given that, AC = BD To show that, ABCD is a rectangle if the diagonals of a parallelogram are equal To show ABCD is a rectangle we have to prove that one of its interior angles is right angled. Proof, In ΔABC and ΔBAD, AB = BA (Common) BC = AD (Opposite sides of a parallelogram are equal) AC = BD (Given) Therefore, ΔABC ≅ ΔBAD [SSS congruency] ∠A = ∠B [Corresponding parts of Congruent Triangles] also, ∠A+∠B = 180° (Sum of the angles on the same side of the transversal) ⇒ 2∠A = 180° ⇒ ∠A = 90° = ∠B Therefore, ABCD is a rectangle. Hence Proved.
Summary: If the diagonals of a parallelogram are equal, we have proved that it is a rectangle.
