Question

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
.

1. ΔBCA Is-congruent-to ΔBFA can be proved by using property of congruence and third angle theorem.

### What is corresponding angel?

Corresponding angles are any two angles that are both on the same side of a transversal that cuts two lines, as well as on the same side of the transversal.

### What is the property of congruence?

If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Because the corresponding angles have the same measure in degrees, we may determine that angle CBA is congruent to angle FBA and that angle CAB is congruent to angle FAB (as evidenced in the given equation). By using the reflexive property of congruence (more precisely, the Third Angle Theorem), we can see that angle BCA and angle BFA are congruent. As a result, since the two triangles share a line segment, we may say that triangle BCA is congruent to triangle BFA since a pair of corresponding angles and the included side are equal (AB).