Question

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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
dropdown. we see that dropdown is
congruent to dropdown by the reflexive property of
congruence. therefore, we can conclude that triangle
bca is congruent to triangle bfa because
dropdown.
options: it is given, of asa, of aaa, of the reflexive property

Explanation:

1. The first blank: The congruence of ∠CBA and ∠FBA, ∠CAB and ∠FAB is given in the problem statement, so we fill "it is given".
2. The second and third blanks: The side AB is common to both triangles ΔBCA and ΔBFA. By the reflexive property of congruence, a segment is congruent to itself, so AB ≅ AB. Thus, the second blank is "AB" and the third blank is "AB".
3. The fourth blank: We have two angles and the included side congruent (∠CBA ≅ ∠FBA, AB ≅ AB, ∠CAB ≅ ∠FAB). This satisfies the Angle - Side - Angle (ASA) congruence criterion. So we fill "of ASA".

Answer:

1. First blank: it is given
2. Second blank: AB
3. Third blank: AB
4. Fourth blank: of ASA