1. The problem asks which pair of congruent corresponding parts is needed to prove that two triangles are congruent using the SAA (Side-Angle-Angle) congruence conjecture. 2. The SAA congruence conjecture states that if two angles and the non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the triangles are congruent. 3. In the given quadrilateral IGHU with diagonal IU, the two triangles to consider are \(\triangle IGU\) and \(\triangle HUU\) (assuming the diagonal IU splits the quadrilateral into two triangles). 4. The angles at vertices I and U are marked congruent, so these two pairs of angles are congruent. 5. To apply SAA, we need the side between these angles or the side opposite one of these angles to be congruent. 6. The pair of congruent corresponding parts needed is the side IU, which is common to both triangles, so it is congruent to itself by the Reflexive Property. 7. Therefore, the pair of congruent corresponding parts needed to prove the triangles congruent by SAA is the side IU and the two angles at vertices I and U. Final answer: The side IU and the two angles at vertices I and U are the congruent corresponding parts needed to prove the triangles congruent by SAA.