To find the correct option that denotes the three pairs of congruent corresponding parts for the triangles \( \triangle ABC \) and \( \triangle A'B'C' \) based on the given conditions, we need to look for pairs of angle and side congruences that show congruence between the two triangles.
Given that \( \triangle ABC \cong \triangle A'B'C' \), we know that:
- Corresponding sides are congruent.
- Corresponding angles are congruent.
Now, let's analyze the options:
Option #1:
- \( \angle A \cong \angle A' \)
- \( \overline{AB} \cong \overline{A'B'} \)
- \( \overline{CB} \cong \overline{A'B'} \) (which actually is incorrect as it repeats \( A'B' \))
Option #2:
- \( \overline{CB} \cong \overline{C'B'} \)
- \( \overline{AC} \cong \overline{A'C'} \)
- \( \angle C' \cong \angle C \) (this doesn’t directly correspond to the correct pairs of angles if we consider triangle matching)
Option #3:
- \( \overline{BC} \cong \overline{B'C'} \)
- \( \angle B \cong \angle C' \)
- \( \angle B' \cong \angle C \) (this is also inconsistent with expected correspondences)
Considering the analysis, there seems to be issues with angle and side correspondence in all options, but we can derive the concept of congruent triangles to test which angles and sides truly correspond.
The correct answer from the items given generally would look like:
- Angles and sides in equal pairings directly corresponding to each other matching triangles.
From the logical breakdown, here’s what we can conclude:
- The answer seems flawed in its presentation. Given what’s commonly found with these triangle properties, unfortunately, based on standard congruency reference, none of the options as presented verify as completely correct.
If finding the best approach from provided options, would project toward potential partial alignments from these over absolute correctness.
Conclusion: Since no options prominently match, the safest answer to select may be Option #1 if taking distinct potential pairing into account, although with noted flaws in correspondence linkage notably on last side written correlation conflicts. Please verify angles and sides in circle, especially around tight congruency brackets potentially common in triangle formulation from given points in queries. Further clarification from characteristics on conformity needs following triangulated congruences in angles and sides laid out here for correctness directly tied back to conventions.