To determine congruence of the two triangles $\triangle ABC$ and $\triangle DEF$ using the Hypotenuse-Leg (HL) Theorem, the following information is required:

HL Theorem Requirements

The Hypotenuse-Leg Theorem states that two right triangles are congruent if:

1. The hypotenuses are congruent (equal in length).
2. One leg of each triangle is congruent.

Key Observations:

• Both triangles $\triangle ABC$ and $\triangle DEF$ are right triangles, as indicated by the right angles.
• We are given:
  • $BC = 28$ (leg of $\triangle ABC$).
  • $EF = 12$ (leg of $\triangle DEF$).
• The hypotenuses $AC$ and $DF$ appear to have matching markings, indicating equality.

Sufficient Information:

To show congruence using the HL Theorem, it must be shown that:

1. The hypotenuse $AC$ is congruent to $DF$ (equal length).
2. One corresponding leg (e.g., $BC = EF$) is congruent.

If this information is confirmed, the two triangles are congruent.

Let me know if you need more clarification or further calculations!

Related Questions:

1. What is the Hypotenuse-Leg (HL) Theorem, and how is it applied?
2. How do you identify the hypotenuse in a right triangle?
3. Can two right triangles be congruent without the HL Theorem?
4. What other congruence theorems apply to triangles (e.g., SSS, SAS)?
5. How can you verify the length of the hypotenuse in each triangle using the Pythagorean Theorem?

Tip: The HL Theorem applies only to right triangles, so always confirm that both triangles have right angles before using it!