Question

Abcd is a parallelogram ab is produced to e so that be = ab .Prove that ed bisects bc

Answer 1

Answer:Given,

ABCD is a parallelogram.

BE = AB

To show,ED bisects BC

Proof:

AB = BE (Given)

AB = CD (Opposite sides of ||gm)

∴ BE = CD

Let DE intersect BC at F.

Now,

In ΔCDO and ΔBEO,

∠DCO = ∠EBO (AE || CD)

∠DOC = ∠EOB (Vertically opposite angles)

BE = CD (Proved)

ΔCDO ≅ ΔBEO by AAS congruence condition.

Thus, BF = FC (by CPCT)

Therefore, ED bisects BC. Proved

hope this helps...