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State the property of congruence and write symbolically the congruency in the correct order for the following triangles

The two triangles shown in the image are \(\triangle XYZ\) and \(\triangle LMN\). Both triangles are right-angled triangles with:

- Hypotenuse \(YZ = MN = 5 \, \text{cm}\)
- One leg \(XY = LM = 3 \, \text{cm}\)
- Right angles at \(X\) and \(L\)

### Property of Congruence:
The triangles are congruent by the **RHS** (Right Angle-Hypotenuse-Side) congruence criterion. This criterion states that if two right-angled triangles have their hypotenuse and one corresponding side equal, the triangles are congruent.

### Symbolic Representation of Congruence:
We can symbolically represent the congruence between the triangles as:
\[
\triangle XYZ \cong \triangle LMN
\]

Would you like further details on how RHS congruence works?

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Here are 5 related questions to explore the topic further:
1. What are the other congruence criteria for triangles?
2. How can we prove two triangles are similar?
3. Why does the RHS criterion specifically apply to right-angled triangles?
4. Can you identify the corresponding angles of the congruent triangles?
5. How would the result change if one of the side lengths was different?

**Tip**: When identifying triangle congruence, always ensure corresponding sides and angles match in the correct order!

State the property of congruence and write symbolically the congruency in the correct order for the following triangles.

Understand how the Right-Angle Hypotenuse-Side (RHS) criterion proves the congruence of triangles XYZ and LMN. Learn the step-by-step explanation of RHS and symbolic representation of congruence. Suitable for students in Grades 8-10.

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