Question

a diagonal of a parallelogram bisects one of its angle.prove that it will bisects its opposite angle also.​

Answer 1

Step-by-step explanation:

Let ABCD is  parallelogram and DB is its diagonal such that DB bisects ∠D. We have to prove that DB bisect ∠B as well.

In Δ  ADB and  Δ CDB

∠1= ∠2                       (Given)

DB = DB                     (common)

∠A= ∠C                      (Opposite angles of a parallelogram)

∴ Δ  ADB ≅  Δ  CDB                 (A.A.S)

∴ ∠ABD = ∠CBD i.e ∠3=∠4      (C.P.C.T)

Hence, DB bisects ∠B as well