MATH SOLVE

5 months ago

Q:
# 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 .

Accepted Solution

A:

Proof: We know that angle CBA is congruent to angle FBA and
that angle CAB is congruent to angle FAB because the corresponding angles have the
same measure in degrees (as evidenced in the given equation). We see that angle
BCA is congruent to angle BFA by the reflexive property of congruence (More
accurately Third Angle Theorem). Therefore, we can conclude that triangle BCA
is congruent to triangle BFA because a pair of corresponding angles and the included side are equal, since the two triangles share a line segment (AB).