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Given: [tex] \angle CBA \cong \angle FBA [/tex]; [tex] \angle CAB \cong \angle FAB [/tex]

Prove: [tex] \triangle BCA \cong \triangle BFA [/tex]

Triangles CBA and FBA share common side BA. Angles CBA and ABF are congruent. Angles CAB and BAF are congruent.

Complete the missing parts of the paragraph proof.

Proof:

We know that angle [tex] \angle CBA [/tex] is congruent to angle [tex] \angle FBA [/tex] and that angle [tex] \angle CAB [/tex] is congruent to angle [tex] \angle FAB [/tex] because they are given.

We see that side [tex] BA [/tex] is congruent to itself by the reflexive property of congruence.

Therefore, we can conclude that triangle [tex] \triangle BCA [/tex] is congruent to triangle [tex] \triangle BFA [/tex] because of the Angle-Side-Angle (ASA) congruence criterion.

Answer :

Equal sides are the paragraph's omission.

What are congruent angles?

  • Angles that are identical to one another are referred to as congruent angles.
  • As a result, these angles have the same measure as one another.
  • The congruence of angles is unaffected by the type of angle, therefore they can be acute, obtuse, exterior, or interior angles.
  • In the fields of architecture, building, design, and fine art, congruent angles are commonly used.
  • An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.
  • The angles of a regular polygon will always be congruent, regardless of its size or scale.

Common Side BA is the Missing Piece of the Proof.

The reasons given in the evidence are sufficient to demonstrate that BCA and BFA are similar.

ΔBFA≅ ΔBCA, but not sufficiently to demonstrate that BCA is compatible with BFA.

To demonstrate congruent triangles, we must demonstrate that the corresponding sides are likewise equal, so we must demonstrate that BA = BA (common side) before the Proof is complete.

Hence, Equal sides are the paragraph's omission.

To learn more about congruent triangles refer to:

https://brainly.com/question/28262429

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