Final answer:
The incorrect statement that is NOT part of the proof is option (b) R is the midpoint of TU. This information is not given and cannot be inferred from the given data; thus, without it, we cannot prove the congruency of triangles QRS and TUS.
Step-by-step explanation:
To prove that triangles QRS and TUS are congruent, one option is to use the Side-Angle-Side (SAS) postulate. If we have two sides and the included angle of one triangle that are congruent to two sides and the included angle of another triangle, the triangles are congruent. Given that S is the midpoint of QT and RU, we can deduce that QS is congruent to ST and RS is congruent to SU (since midpoints create segments of equal length).
However, we have no information about angles or the position of point R relative to point T and line segment SU, so statement (d), 'The angles in QRS and TUS are congruent,' is not necessarily part of the proof and cannot be assumed without additional information. Therefore, to correctly complete the proof, we would need more data regarding the angles or the other side lengths of the triangles.
The incorrect statement that is NOT part of the proof is thus option (b) R is the midpoint of TU, which is not given and cannot be inferred from the given statements. Without knowing that R is the midpoint of TU, we cannot conclude the triangles are congruent because we do not have enough information to apply SAS or any other congruence postulate or theorem.