The image shows two right triangles, △BAC and △DAC, with right angles at points B and D. The question asks what else is needed to prove the triangles congruent using the Hypotenuse-Leg (HL) theorem.

The HL theorem states that two right triangles are congruent if their hypotenuses are congruent and one leg is congruent.

In the image:

• Both triangles have right angles at B and D.
• Line segment AC is common to both triangles, meaning AC is the hypotenuse for both triangles.

To apply the HL theorem, we also need to know if one pair of corresponding legs is congruent. The second option in the answer choices, BA ≅ DA, provides this missing piece of information.

Conclusion:

The correct answer is: BA ≅ DA.

Would you like more details on how the HL theorem works or any additional clarifications?

Here are 5 related questions to consider:

1. What are the specific conditions for applying the Hypotenuse-Leg theorem?
2. How does the HL theorem differ from the other triangle congruence criteria like SAS or ASA?
3. Can the HL theorem be used for triangles that are not right triangles?
4. What other methods could prove triangle congruence in this situation if the HL theorem didn't apply?
5. What is the significance of the common hypotenuse in proving triangle congruence?

Tip: When using the HL theorem, always check if the hypotenuses and a corresponding leg are given as congruent, as this is key for applying it effectively.