Question 935635
We have 
<FGH = <EGH (given)
<GFH = <GEH (triangle EFG is isosceles) 
GH is a shared side 

=> Triangle FGH is congruent to triangle EGH (AAS situation) 
=> side HF = side HE (congruent triangles properties, corresponding sides are equal) 
=> H is the midpoint of EF