Question

19. In the given figure, AD = AE, BD= EC. Prove that triangle ABC 1s an isosceles triangle​

Answer 1

Answer:

IN triangle ADE,

AD = AE

therefore,

∠ADE = ∠AED

∠ADB + ∠ADE = 180

∠AEC + ∠AED = 180

∠AEC + ∠ADE = 180 ( ∠AED = ∠ADE )

180 - ∠ADE = ∠ADB

180 - ∠ADE = ∠AEC

∴ ∠ADB = ∠AEC

in triangle ABD, ACE,

AD = AE

BD = CE

∠ADB = ∠AEC

∴ΔABD ≅ Δ ACE

∴ AB = AC (CPCT)

∴ ΔABC is an isosceles triangle