https://file.aiquickdraw.com/mathbot/file/1739944581843q1vjnrwu.jpg

The task in the image asks you to prove that triangles \( \triangle XYZ \) and \( \triangle ZWX \) are congruent.

Here's how we can approach this:

1. **Right Angles:** Both triangles have a right angle at vertex \( Z \), as shown by the square symbols at \( Z \). This gives us \( \angle XYZ = \angle ZWX = 90^\circ \).

2. **Shared Side:** The two triangles share side \( XZ \), which means \( XZ = XZ \) by the reflexive property.

3. **Right-Angle Hypotenuse-Leg (RHL) Theorem:** Since both triangles have a right angle and share a common hypotenuse, and their legs (segments \( XY \) and \( XW \)) are equal, we can conclude that the triangles are congruent by the Right-Angle Hypotenuse-Leg Theorem.

Therefore, we can prove that:
\[
\triangle XYZ \cong \triangle ZWX
\]

Let me know if you need further details or have any other questions!

Here are 5 related questions you might find useful:
1. What is the Reflexive Property in geometry?
2. Can the Right-Angle Hypotenuse-Leg Theorem be applied to non-right triangles?
3. What other triangle congruence theorems exist besides RHL?
4. How do we prove triangle congruence using SSS (Side-Side-Side)?
5. What are the differences between congruent and similar triangles?

**Tip:** Always check for shared sides and angles when trying to prove triangle congruence—it's often the key to finding the solution.

Prove that \( \triangle XYZ \cong \triangle ZWX \).

Learn how to prove triangle congruence for right-angled triangles using the Right-Angle Hypotenuse-Leg (RHL) Theorem. This problem involves key concepts such as shared sides and right angles, suitable for students in Grades 9-11.

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