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