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

In ∆AEB and ∆BDC

EB = BC [Given]

∠ABE = ∠DCB [Corresponding angles]

AB = DC [Opposite sides of || gm ABCD are equal]

Thus, ∆AEB ≅ ∆BDC by S.A.S axiom

So, by C.P.C.T

BD = AE

In || gm ABCD,

BC = AD (As opposite sides of || gm are equal)

Given,

BC = BE

∴ AD = BE.

Since, opposite sides of quadrilateral AEBD are equal (i.e., BD = AE and AD = BE)

Hence, proved that AEBD is a parallelogram.