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

Prove: △AHG ~ △CHD

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