1. **Problem Statement:** Determine which theorem can be used to show that triangle ABC is congruent to triangle DEF given that side AB equals side DE, side AC equals side DF, and both triangles have right angles at C and F respectively. 2. **Relevant Theorems:** - **AAS (Angle-Angle-Side):** Two angles and a non-included side are congruent. - **SSS (Side-Side-Side):** All three sides are congruent. - **ASA (Angle-Side-Angle):** Two angles and the included side are congruent. - **HL (Hypotenuse-Leg):** For right triangles, if the hypotenuse and one leg are congruent, the triangles are congruent. 3. **Given Information:** - Triangles ABC and DEF are right triangles with right angles at C and F. - Side AB = side DE (hypotenuses). - Side AC = side DF (one leg). 4. **Applying the HL Theorem:** - HL theorem 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. - Here, AB and DE are hypotenuses, AC and DF are legs, and both triangles have right angles. 5. **Conclusion:** - By the HL Triangle Congruence Theorem, triangle ABC is congruent to triangle DEF. **Final answer:** D. HL Triangle Congruence Theorem