Question

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
. 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: Identify Given Angles

The first blank is filled with "they are given" since \( \angle CBA \cong \angle FBA \) and \( \angle CAB \cong \angle FAB \) are given in the problem.

Step2: Reflexive Property Side

The side \( \overline{BA} \) is congruent to \( \overline{BA} \) by the reflexive property (a side is congruent to itself). So the second and third blanks are \( \overline{BA} \) and \( \overline{BA} \) respectively.

Step3: Triangle Congruence Criterion

We have two angles and the included side (ASA: Angle - Side - Angle) congruent. The two angles are \( \angle CBA \cong \angle FBA \), \( \angle CAB \cong \angle FAB \), and the included side \( \overline{BA} \cong \overline{BA} \). So the triangle congruence criterion is ASA.

Answer:

First blank: they are given; Second blank: \( \overline{BA} \); Third blank: \( \overline{BA} \); Fourth blank: ASA (Angle - Side - Angle) congruence criterion