Given: ∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB

Prove: ΔBCA Is-congruent-to ΔBFA

Triangles C B A and F B A share common side B A. Angles C B A and A B F are congruent. Angles C A B and B A F are congruent.

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

. 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

.

congruent triangles, we must demonstrate that the corresponding sides are likewise equal.