In a pentagon ABCDE,
AB = AE
BC = ED
BD = EC
Prove that AC = AD
(1) Triangle EDC is congruent to triangle BCD (SSS).
(2) Since angles in the same segment are equal(angle DEC = angle DBC), we can deduce that this pentagon is inscribed in a circle.
(3) Chords AB=AE implies arc AB=AE , angle,x subtended by these arcs are the same. Similarly, BC=ED, angle,y subtended will be the same too.
angle ADC=angle ACD= x+y and since base angles are equal, triangle ADC is an isosceles triangle.