Which of the following proves these triangles are congruent?

It looks like you're referring to a specific problem with multiple options to determine which one proves that two triangles are congruent. However, I don't have the details of the triangles or the options provided. To help you effectively, here are the common **triangle congruence criteria** that are typically used to prove that two triangles are congruent: 1. **Side-Side-Side (SSS):** If all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent. 2. **Side-Angle-Side (SAS):** If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. 3. **Angle-Side-Angle (ASA):** If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. 4. **Angle-Angle-Side (AAS):** If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent. 5. **Right Angle-Hypotenuse-Side (RHS) or Hypotenuse-Leg (HL) for Right Triangles:** If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent. If you provide the specific options or a description of the triangles in question, I can give a more targeted answer on which criterion applies.