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 .

Answer 1

Missing Part in Proof is Equal Sides ( common side)

Step-by-step explanation:

Missing Part of the proof is Common Side BA

As Reason mentioned in proof are enough to show that

ΔBCA Is Similar to ΔBFA

ΔBCA  ≈ ΔBFA

but not enough to show that

ΔBCA Is-congruent-to ΔBFA

ΔBCA  ≅ ΔBFA

to Show congruent triangles we need to show that corresponding sides are also equal

so we need to show that BA = BA  ( common side)

then Proof will be complete

Hence missing Part in Proof is Equal Sides ( common side)

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Answer 2

Given

$BA\cong BA$

ASA postulate

Step-by-step explanation:

In triangle BCA and BFA

$BA\cong BA$

Reason: Reflexive property

$\angle CBA\cong \angle FBA$

Reason: Given

$\angle CAB\cong \angle FAB$

Reason: Given

$\triangle$BCA$\cong$$\triangle$BFA

Reason: ASA postulate

ASA postulate: When two angles and  side on which two angles are made  of one triangle are congruent its corresponding angles and corresponding side then two triangles are congruent by ASA postulate.

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