Question

In the given figure AD = AE, BD = EC, and angle ade=angleacb prove that ABC is an isosceles triangle.

Answer 1

NOTE:

Hi. I don't know the figure, but I have made it. It is at bottom of my answer.

ANSWER:

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 ]