Question

In the adjoining figure, ABCD is a parallelogram. CB is produced to E such that BE=BC.prove that AEBD is a parallelogram

Answer 1

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

Answer 2

REFER TO THE ATTACHMENTS...