Question

given: ∠cba ≅ ∠fba; ∠cab ≅ ∠fab
prove: △bca ≅ △bfa
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

Explanation:

Step1: State given information

They are given in the problem statement.

Step2: Identify common side

Side $\overline{BA}$ is common to both $\triangle BCA$ and $\triangle BFA$, so $\overline{BA}\cong\overline{BA}$ by the reflexive - property of congruence.

Step3: Apply congruence criterion

Since we have two pairs of congruent angles ($\angle CBA\cong\angle FBA$ and $\angle CAB\cong\angle FAB$) and a common side ($\overline{BA}\cong\overline{BA}$), we can use the Angle - Side - Angle (ASA) congruence criterion.

Answer:

We know that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB because it is given. We see that $\overline{BA}$ is congruent to $\overline{BA}$ by the reflexive property of congruence. Therefore, we can conclude that triangle BCA is congruent to triangle BFA because ASA (Angle - Side - Angle) congruence criterion.