ABC is a equilateral triangle D and E are mid-points of AB and AC respectively and DF = FE, then prove \$\triangle ADF \cong \triangle AEF\$.

P is the mid-point of MO and PN is the angle bisector of \$\angle N\$. Prove \$\triangle MNP \cong \triangle ONP\$.

C is the mid point of AB, AC = CB = DC = EC. Prove \$\triangle ADC \cong \BEC\$.

H is the mid-point of EG and EH = HF = HG. Prove \$\triangle HEF \cong \triangle HGF\$.

If G is the mid-point of EF then prove \$\triangle DGE \cong \triangle DGF\$.