If three angles of a quadrilateral are 90° each, show that the given

1.	If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Answer» The given quadrilateral ABCD will be a rectangle, if its each angle is 90° Since, the sum of interior angles of a quadrilateral is 360°. ∴∠A +∠B + ∠C + ∠D = 360° ⇒ 90° + 90° + 90° + ∠D = 360° ⇒ 270° + ∠D = 360° ⇒ ∠D = 360° – 270° ⇒ ∠D = 90° Since, each angle of the quadrilateral is 90°. ∴ The given quadrilateral is a rectangle.

If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.

Answer»

The given quadrilateral ABCD will be a rectangle, if its each angle is 90°

Since, the sum of interior angles of a quadrilateral is 360°.

∴∠A +∠B + ∠C + ∠D = 360°

⇒ 90° + 90° + 90° + ∠D = 360°

⇒ 270° + ∠D = 360°

⇒ ∠D = 360° – 270°

⇒ ∠D = 90°

Since, each angle of the quadrilateral is 90°.

∴ The given quadrilateral is a rectangle.