Since AB = AC, the angles ABC = ACB = 72°
Bisecting angle ABC means that angle ABD = angle BAD = 36°
Therefore....in triangle ABD......AD = BD
And the thitd angle in this triangle, BDA = 108°
So angle BDC = 180 - 108° = 72°
And angle ACB = DCB = 72°
So.....in triangle BDC, angle DCB = angle BDC
So BD = BC
So
BC = BD = AD
