In triangle ABC points D and E are on bc such that BD=EC and AD=AE prove that AB=AC

In triangle ADE ,

AD = AE [given]

⇒ ∠AED = ∠ADE [angles opposite to equal sides are equal]

⇒ 180 - ∠AED = 180 - ∠ADE

⇒∠AEC = ∠ADB ............(1)

in Δ ABD and Δ ACE

AD = AE [ given ]

∠ADB = ∠AEC [ using (1) ]

BD = CE [ GIVEN ]

Δ ABD is congruent to Δ ACE [ SAS ]

⇒ AB = AC [ CPCT ]

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