Based on the given figure above, the criteria for triangle congruence that can be used to prove the pair of triangles below are congruent would be SAS or Side-Angle-Side Triangle congruence. Hope this is the answer that you are looking for. Have a great day!
When there are 2 right angles at the base, like there is in your picture, along with the legs being equal as well as the sharing line, the answer is HL.
