https://file.aiquickdraw.com/mathbot/file/1726005961257x1gtfgjb.jpg

The problem asks you to determine what additional information is required to know if two triangles are congruent using the HL (Hypotenuse-Leg) theorem.

Here are the key features of the problem:

1. **Given Triangles**: The diagram shows two right-angled triangles, \( \triangle WVX \) and \( \triangle ZYX \), with shared segment \( XZ \), which seems to represent the right angle.
   
2. **HL Theorem**: The Hypotenuse-Leg theorem applies to right-angled triangles. It states that two triangles are congruent if their hypotenuses and one corresponding leg are congruent.

To apply the HL theorem, we need to know:
- That both triangles are right-angled.
- The hypotenuses of the two triangles are congruent.
- One leg from each triangle is congruent.

In this case, since both triangles appear to be right-angled, and they share one leg \( XZ \), we need to confirm the congruence of the hypotenuses.

### Answer: 
- **Option 1**: \( \overline{VW} \cong \overline{ZY} \) is the correct additional information.
   - These represent the hypotenuses of the two triangles, and proving them congruent would satisfy the Hypotenuse-Leg criterion for triangle congruence.

Let me know if you'd like more details!

---

Here are 5 questions to extend this problem:

1. What is the Hypotenuse-Leg (HL) theorem and how is it used in triangle congruence?
2. How can you determine congruence of right triangles using the hypotenuse and a leg?
3. What are the other triangle congruence theorems besides HL?
4. How does sharing a leg in a triangle impact the congruence proof?
5. Why is proving the hypotenuse congruent necessary in the HL theorem?

**Tip**: When working with right triangles, the HL theorem is often quicker than other congruence theorems!

State what additional information is required in order to know if the triangles are congruent using the HL theorem.

Learn how to determine triangle congruence using the HL (Hypotenuse-Leg) theorem. This problem focuses on congruence in right triangles and requires knowledge of triangle sides and angles. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation