If Point C and D are equidistant from point A, it means that AC and AD are of the same length. AC = AD
AC = AD (S) (Points C and D are equidistant from point A)
AE = AE (S) (The two triangle shared the same side)
∠CAE = ∠EAD (A) (This angle is between the two sides that we just proved to be equal)
By SAS,
ΔEAD ≡ ΔEAC