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Write a similarity statement relating the three triangles.

To write a similarity statement relating the three triangles in the given figure, we need to identify the corresponding angles that make the triangles similar. The figure shows three right triangles: \( \triangle JKL \), \( \triangle JKN \), and \( \triangle LNK \).

1. **\(\triangle JKL\) and \(\triangle JKN\):**
   - Both triangles share angle \( \angle J \).
   - Both triangles have a right angle (\( \angle JKN = \angle JKL = 90^\circ \)).

2. **\(\triangle JKL\) and \(\triangle LNK\):**
   - Both triangles have right angles (\( \angle JKL = \angle LNK = 90^\circ \)).
   - Both triangles share angle \( \angle L \).

3. **\(\triangle JKN\) and \(\triangle LNK\):**
   - Both triangles have right angles (\( \angle JKN = \angle LNK = 90^\circ \)).
   - Both triangles share angle \( \angle K \).

Since the triangles share two pairs of corresponding angles, the triangles are similar by the AA (Angle-Angle) similarity criterion. The similarity statements are:

\[ \triangle JKL \sim \triangle JKN \]
\[ \triangle JKL \sim \triangle LNK \]
\[ \triangle JKN \sim \triangle LNK \]

Would you like further details or have any questions about this explanation?

Here are 5 questions you might ask:
1. How do you determine the similarity of triangles?
2. Can you explain the AA similarity criterion in more detail?
3. What are other similarity criteria for triangles?
4. How can you apply similarity in solving real-world problems?
5. Can you solve an example problem using similar triangles?

**Tip:** When working with similar triangles, remember that the ratios of corresponding sides are equal. This property can be very useful for solving for unknown lengths.

Learn how to write a similarity statement relating three triangles using the AA (Angle-Angle) similarity criterion. This problem involves identifying corresponding angles and applying the principle of triangle similarity. Suitable for students in Grades 9-12 studying geometry.

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