Mathematics
In the given figure; AB = BC and AD = EC. Prove that : BD = BE.
Triangles
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Answer
Given,
⇒ AD = EC
⇒ AD + DE = EC + DE
⇒ AE = DC
In △ ABE and △ BDC,
⇒ AB = BC (Given)
⇒ ∠A = ∠C (Since, AB = BC and angles opposite to equal angles are equal)
⇒ AE = DC (Proved above)
∴ Δ ABE ≅ Δ BDC (By S.A.S. axiom)
We know that,
Corresponding parts of congruent triangle are equal.
⇒ BE = BD.
Hence, proved that BD = BE.
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