Como se muestra en la figura , los puntos $D,E,F$ lies the sides $AB$ , $BC$ , $CA$ of the acute angle $\vartriangle ABC$ respectively. If $\angle EDC = \angle CDF$ , $\angle FEA=\angle AED$ , $\angle DFB =\angle BFE$ , prove that the $CD$ , $AE$ , $BF$ are the altitudes of $\vartriangle ABC$ .