Question

prove that the diagonals of a rectangle are equal

Answer 1

Hey there !

Solution:

Refer to the attachment for diagram.

Given : ABCD is a rectangle.

To Prove : AC = BD

Construction : Join AC and BD

Proof :

Consider Δ ADC and Δ BCD

We know that, in a rectangle opposite sides are equal and all the angles are 90°. Hence,

AD = BC ( S )

∠ADC = ∠BCD ( A )

CD = CD ( S )  [ Common Side ]

Therefore by SAS Congruence Criterion, Δ ADC ≅ Δ BCD. By CPCT, AC = BD.

Hence the diagonals are equal.

Hence Proved !

Hope it helped !

Answer 2

Step-by-step explanation:

Given:

• A rectangle ABCD in which AC and BD are Diagonals.

To Prove:

• Diagonals are equal i.e AC = BD

Proof: In ∆ABD & ∆BAC , we have

• AB = BA { These sides are common in both triangles }
• ∠A = ∠B { Each side of a rectangle is of 90° }
• AD = BC { Opposite Sides of a rectangle are equal to each other }

∴ ∆ABD ≅ ∆BAC ( By Side Angle Side SAS criteria )

Hence, BD = AC