1. The problem asks for the possible criteria for using the Law of Cosines. 2. The Law of Cosines is used to find unknown sides or angles in a triangle when you have: - Two sides and the included angle (SAS) - All three sides (SSS) 3. The Law of Cosines formula is: $$c^2 = a^2 + b^2 - 2ab \cos(C)$$ where $a$, $b$, and $c$ are sides of the triangle and $C$ is the angle opposite side $c$. 4. Important rules: - SAS (Side-Angle-Side): You know two sides and the included angle. - SSS (Side-Side-Side): You know all three sides. 5. Other criteria like ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSA (Side-Side-Angle) do not use the Law of Cosines directly; ASA and AAS use the Law of Sines, and SSA can be ambiguous. 6. Therefore, the possible criteria for the Law of Cosines are **SSS and SAS**. Final answer: SSS, SAS