We are asked to prove that △ EFG is congruent to △ HFG if we know that EF≅HF and that G is the midpoint of EH. Since a midpoint divides a segment into two congruent segments, HG and GE are congruent.
By the Reflexive Property, we know that FG≅FG. Therefore, △ EFG has all three sides that are congruent to the sides of △ HFG. This means that these triangles are congruent by the Side-Side-Side Congruence Theorem.
