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.


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 ≅ 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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