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

Prove: △AHG ~ △CHD

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