Question

In the given figure, AD = AE and BD = EC.
Prove that AB = AC.
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Answer 1

Given,

AD=AE  where, D and E are points on BC,

Such that BD = EC,

To prove :

AB = AC,

Proof :

∵ AD=AE

⇒ ∠ADE = ∠AED

⇒ 180° -  ∠ADE =  180° -  ∠AED

⇒ ∠ADB = ∠AEC,

BD = EC ( given )

By SAS postulate of congruence,

Δ ABD ≅ Δ ACE

By CPCT,

AB = AC

Hence, proved.....