Question

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

Answer 1

Given: ABCD is a parallelogram. AC = BD
To Prove: ABCD is a rectangle.

Proof: In ΔABC and Δ BAD,
AB = BA (common side)
AC = BD (given)
AD = BC (opposites sides of a ||gm)

∴ ΔABC ≅ Δ BAD (by SSS congruence rule)
∴ ∠ABC = ∠BAD (CPCT) ... (i)

∵ AD || BC, AB intersects them. ∠ABC and∠BAD form interior angles on the same side.

⇒ ∠ABC + ∠BAD = 180°
⇒ 2∠ABC = 180°
⇒ ∠ABC = ∠BAD = 90°
If one of the angle of a paralleogram is right angle, it is a rectangle.
Hence ABCD is a rectangle.

Answer 2

This is your answer to the question.