1. **Problem:** Select all the sets of conditions that will form only one unique triangle. 2. **Understanding the problem:** We need to identify which sets of given conditions guarantee exactly one unique triangle. 3. **Triangle uniqueness rules:** - **ASA (Angle-Side-Angle):** Two angles and the included side form exactly one unique triangle. - **SAS (Side-Angle-Side):** Two sides and the included angle form exactly one unique triangle. - **SSS (Side-Side-Side):** All three sides form exactly one unique triangle. - **AAS (Angle-Angle-Side):** Two angles and a non-included side also form one unique triangle. - **AAA (Angle-Angle-Angle):** All three angles only determine similarity, not uniqueness (infinite similar triangles). 4. **Analyzing each condition:** - Two angles and an included side (ASA): forms one unique triangle. - Two sides and a nonincluded angle (SSA): may form zero, one, or two triangles (ambiguous case). - Two sides and an included angle (SAS): forms one unique triangle. - All three angles (AAA): does not form a unique triangle, only similar triangles. - All three sides (SSS): forms one unique triangle. 5. **Final answer:** The sets that form only one unique triangle are: - Two angles and an included side - Two sides and an included angle - All three sides \textbf{Answer:} \text{Two angles and an included side, Two sides and an included angle, All three sides}