The correct option is D (b) or (c) above.
In the triangles △ADB and ΔADC,
AD is the common side
BD = DC (Since D is the midpoint of BC)
Hence ratio of corresponding sides is:
ADAD=1,
BDDC=1,
ABAC
For the triangles to be similar, all three ratios should be equal.
⟹ABAC=1
AB=AC
Since opposite angles to equal sides in isoceles triangle are equal.
⟹∠B=∠C
Hence one of the conditions is enough as the other can be inferred from either Option B or Option C.