1. The problem asks to identify the triangle congruence criteria shown in the diagram with two right triangles sharing a hypotenuse and a leg. 2. The key congruence criteria for right triangles include HL (Hypotenuse-Leg), ASA (Angle-Side-Angle), SSA (Side-Side-Angle), and AAS (Angle-Angle-Side). 3. HL states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. 4. ASA requires two angles and the included side to be congruent. 5. SSA is generally not a valid congruence criterion except in special cases. 6. AAS requires two angles and a non-included side to be congruent. 7. Since the diagram shows two right triangles with congruent hypotenuse and one leg, the correct congruence criterion is HL. Final answer: HL