If the angle of a quadrilateral are equal, prove that it is a rectangle.

Question

KnowledgeBoat · Accepted Answer

Suppose there is a quadrilateral ABCD. Let ∠A = ∠B = ∠C = ∠D = x So, ∠A = ∠C and ∠B = ∠D (Opposite angles are equal) ∴ ABCD is a parallelogram. Since, sum of angles in a quadrilateral = 360° ⇒ ∠A + ∠B + ∠C + ∠D = 360° ⇒ x + x + x + x = 360° ⇒ 4x = 360° x = ⇒ x = 90°. ∴ ∠A = ∠B = ∠C = ∠D = 90°. Since, each angle = 90°, Hence, proved that ABCD is a rectangle.

Mathematics

If the angle of a quadrilateral are equal, prove that it is a rectangle.

Rectilinear Figures

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