Given: Parallelogram ABCD, AC bisects angle FAB, AG=AE

Prove: Triangle AHG ~ Triangle CHD

Definition
Substitution
angle AGH = angle CDE and angle GAH = angle DCA
angle CAB = angle DCA, angle CDE = angle AED
Definition
angle AGE = angle AED
If two sides of a triangle are equal, the angles opposite them are equal
Triangle AHG ~ Triangle CHD
AA similarity
angle FAC = angle CAB
DC || AB
Parallel lines form equal alternate interior angles