Prove that each angle of a rectangle is 90°.

We know that opposite sides of a rectangle are equal.

∴ AD = BC and AB = CD

Also, the diagonals of rectangle are equal.

∴ AC = BD

Now, consider ΔADC and ΔBCD

⇒ AD = BC

⇒ AC = BD

⇒ DC = DC [Common]

∴ ΔADC ≅ ΔBCD by SSS congruency rule.

∴ ∠ ADC = ∠BCD = x (let) [By C.P.C.T.]

But, adjacent sides of a parallelogram are supplementary. [∵ rectangle is a parallelogram].

∴ ∠ADC + ∠BCD = 180°

⇒ x + x = 180°

⇒ 2x = 180°

⇒ x = 90°

⇒ ∠ADC = ∠BCD = 90°.

Since, opposite angles of a parallelogram are also equal.

∴ ∠DAB = ∠BCD = 90° and ∠ABC = ∠ADC = 90°.

Hence, proved that each angle of a rectangle is 90°.