1. **State the problem:** We need to determine which information can be used to prove that triangle ABC is congruent to triangle DEF. 2. **Given information:** - Triangle ABC has a right angle at C. - Triangle DEF has a right angle at F. - Side AB is congruent to side DE (both marked with the same hash). - Side BC is congruent to side EF (both marked with a single hash). 3. **Recall the congruence criteria for right triangles:** - The Hypotenuse-Leg (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. 4. **Identify hypotenuses and legs:** - In triangle ABC, the hypotenuse is AB (opposite the right angle at C). - In triangle DEF, the hypotenuse is DE (opposite the right angle at F). 5. **Check given congruences:** - AB ≅ DE (hypotenuses congruent). - BC ≅ EF (legs congruent). 6. **Check right angles:** - ∠C is right angle in ABC. - ∠F is right angle in DEF. 7. **Conclusion:** Using HL theorem, triangles ABC and DEF are congruent if we know: - AB ≅ DE (given) - BC ≅ EF (given) - ∠F is a right angle (D) 8. **Evaluate each option:** - A: m∠D + m∠E = 90° (not directly useful for congruence here) - B: m∠D = 37° (not necessary for HL congruence) - C: ∠E ≅ ∠B (not necessary for HL congruence) - D: ∠F is a right angle (necessary to confirm right triangle and apply HL) **Final answer:** Only options B and D provide necessary information to prove congruence using HL theorem, but since B is not necessary, the key is D. **Therefore, the information that can be used to show ABC ≅ DEF is:** - Side AB ≅ DE (given in figure) - Side BC ≅ EF (given in figure) - ∠F is a right angle (option D) Hence, the correct selections are **D** and the given side congruences from the figure.