Question

(1) If ABCD is a rectangle in which the diagonal BD bisects angel B, then show that ABCD is a square.​

Answer 1

Answer:

Given :

• ABCD is a rectangle
• Diagonal BD bisects angel

To Prove :

• ABCD is a aquare

Solution :

ABCD is a rectangle where BD bisects ∠B

Therefore,

• AB = DC
• CB = AD

In ∆ABD and ∆BCD

AD = BC (Given)

AB = DC (Given)

∠DAB = ∠DCB (90°)

∴ ∆ABD ≅ ∆BCD (By SAS Congruency)

AD = CD (C.P.C.T)

Hence, all sides are equal

∴ ABCD is a square