We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because . We see that is congruent to by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because .

The triangles share side BA, so BA is congruent to itself by the reflexive property. This is the side needed along with the two given pairs of congruent angles, ∠CBA ≅ ∠FBA and ∠CAB ≅ ∠FAB. The triangles are therefore congruent by ASA; the shared side is side BA.

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