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

Prove: △AHG ~ △CHD

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