High School

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Given: ∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB
Prove: ΔBCA ≅ ΔBFA

Complete the missing parts of the paragraph proof.

Proof:
We know that angle ∠CBA is congruent to angle ∠FBA and that angle ∠CAB is congruent to angle ∠FAB because they are given. We see that segment AB is congruent to segment AB by the reflexive property of congruence. Therefore, we can conclude that triangle ΔBCA is congruent to triangle ΔBFA because of the ASA (Angle-Side-Angle) congruence postulate.

Answer :

The congruence between triangles BCA and BFA is explained by the ASA Congruence Postulate, with two pairs of congruent angles given and the included side being the same in both triangles.

Proof: We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because they are given in the problem statement. We see that side AB is congruent to side BA by the reflexive property of congruence, since it is the same side in both triangles.

Therefore, we can conclude that triangle BCA is congruent to triangle BFA because of the ASA (Angle-Side-Angle) Congruence Postulate, which states that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.

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