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For each pair of triangles, determine whether the Hypotenuse-Leg (HL) Congruence Property can be used to prove that the triangles are congruent.
If necessary, you may learn what the markings on a figure indicate.



Let's go over each pair of triangles to determine if the Hypotenuse-Leg (HL) Congruence Property can be applied.

The **HL Congruence Theorem** states that two right triangles are congruent if:
1. They both have a right angle.
2. The hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle.

Now, I'll analyze each pair from the image:

1. **Pair (a)**: 
   - Both triangles have a right angle (marked by the square in the corner).
   - The hypotenuses are congruent (the diagonal side is marked with the same line in both triangles).
   - One leg in each triangle is congruent (the horizontal legs have the same marking).
   - **Conclusion**: Yes, the HL Congruence Property can be used.

2. **Pair (b)**:
   - Both triangles have a right angle (the square marking).
   - The hypotenuse is congruent (25 cm in both triangles).
   - One leg (the side marked as 15 cm) is also congruent in both triangles.
   - **Conclusion**: Yes, the HL Congruence Property can be used.

3. **Pair (c)**:
   - Both triangles are not right triangles (no right angle is marked).
   - Since the HL property only applies to right triangles, **this pair is not eligible**.
   - **Conclusion**: No, the HL Congruence Property cannot be used.

4. **Pair (d)**:
   - These triangles do not have a right angle (no square marking indicates a right angle).
   - Therefore, the HL property cannot apply here.
   - **Conclusion**: No, the HL Congruence Property cannot be used.

### Summary:
- **(a)**: Yes
- **(b)**: Yes
- **(c)**: No
- **(d)**: No

Would you like more details or have any other questions? Here are some related questions you might find useful:
1. What are the differences between the HL property and the SAS (Side-Angle-Side) congruence theorem?
2. Can you use the HL Congruence Theorem in non-right triangles?
3. What are the other congruence properties used for proving triangles congruent?
4. How can you determine if two triangles are congruent using the SSS (Side-Side-Side) theorem?
5. How can you use the Pythagorean theorem to verify the hypotenuse?

**Tip**: Always look for the right angle marking when trying to apply the HL Congruence Property—it only works with right triangles!

For each pair of triangles, determine whether the Hypotenuse-Leg (HL) Congruence Property can be used to prove that the triangles are congruent. If necessary, you may learn what the markings on a figure indicate.

Determine whether the Hypotenuse-Leg (HL) Congruence Property can be applied to prove triangle congruence. This problem involves right triangles, markings, and congruence properties, suitable for students in Grades 9-10.

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