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