DE is perpendicular to AB
∴∠E=90o
DF is perpendicular to AC
∴∠F=90o
If we consider two triangles so formed, ΔDEB and ΔCFD, then their hypotenuse BD and CD are equal.
∠E=∠F=90o. Also DE=CF.
Thus according to R.H.S condition of congruence ΔDEB≅ΔCFD
Thus, the corresponding angles ∠B and ∠C are equal, i.e ∠B=∠C