Question

Prove logically that the diagonal of a rectangle are equal.

Answer 1

Proof :

ABCD is a rectangle and AC and BD

are it's diagonals.

We want know AC = BD

ABCD is a rectangle , means ABCD is a

parallelogram with all its angles equal

to right angle.

Consider the triangles ∆ABC and ∆BAD

AB = BA ( Common )

<B = <A = 90° [ Each angle of rectangle ]

BC = AD [ Opposite sides of the rectangle]

Therefore ,

∆ABC congruent to ∆BAD

=> AC = BD

or the diagonals of a rectangle are

equal .

•••••

Answer 2

Let ABCD be a rectangle.

Then AC and BD are the diagonals.

To Prove: AC=BD

Proof : In △ABC and △ABD

∠ABC = ∠BAD [90⁰]

BC=AD [Opp. Sides]

AB=AB [Common side]

△ABC ≅ △ABD[SAS]

AC=BD

Hence proved✅.