∠ AGH = ∠ CDE and ∠ GAH = ∠ DCA

Definition

AA similarity

∠ CAB = ∠ DCA, ∠ CDE = ∠ AED

Substitution

∠ AGE = ∠ AED

If two sides of a triangle are equal, the angles opposite them are equal

△AHG ~ △CHD

Definition

∠ FAC = ∠ CAB

DC ǁ AB

Parallel lines form equal alternate interior angles