Prove that the diagonals of a rectangle are of equal length

Dhanalakshmi · July 2, 2019, 11:18am

Prove that the diagonals of a rectangle are of equal length.

Dhanalakshmi · July 2, 2019, 11:25am

ABCD is a rectangle with AC and BD as its diagonals.
ABCD is a rectangle
∴∠A = 90^o, AD = BC
AD//BC and AB is a transversal
∴∠A +∠B = 180^o
⇒ ∠B = 90^o
In ∆ ABD and ∆ BAC
AB = BA
∠A = ∠B
AD = BC
∴∆ABD ∆BAC
⇒ BD = AC (c.p.c.t)
Hence, the diagonals of a rectangle are equal.