To use the ASA (Angle-Side-Angle) Congruence Theorem, one must show that two angles and the side included between them in one triangle are congruent to the corresponding angles and side in the other triangle.
In this case, the given information includes:
- ∠B ≅ ∠R (one angle)
- ¯AB¯ ≅ QR¯ (the side between the two angles)
- ¯BC¯ ≅ RS¯ (another side)
- ∠C ≅ ∠S (another angle)
In the given information, there are actually two angles (∠B and ∠C) that are congruent to two angles in triangle QRS (∠R and ∠S), and there's one included side (¯AB¯ ≅ QR¯).
However, to use the ASA theorem, Omari needs the angles to be paired such that the side lies between them. With the existing information, the needed angle-side-angle format isn't met because there is no side that is included between ∠B and ∠C.
Therefore, the missing information is that the angle ∠A needs to be included with the sides and angles in the congruence for the ASA theorem to apply correctly.
In conclusion, he needs the congruence of angle ∠A (or the corresponding angle in triangle QRS that would align correctly) to fully utilize ASA congruence theorem.