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
.

Answers

1. kimchi2
ΔBCA ≅ ΔBFA, to prove congruent of triangle missing Part in Proof is Equal Sides ( common side).
Common Side BA is the Missing Piece of the Proof.
The reasons given in the evidence are sufficient to demonstrate that
ΔBCA Is Similar to ΔBFA
ΔBFA ≈ ΔBCA,
but not sufficiently to demonstrate that
ΔBCA is compatible with ΔBFA.
ΔBCA ≅ ΔBFA:
To demonstrate congruent triangles, we must demonstrate that the corresponding sides are likewise equal.
Consequently, we must demonstrate that
BA = BA (common side) in order for the proof to be complete.
Hence missing Part in Proof is Equal Sides ( common side)

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