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To determine which statement is valid, we need to check whether triangles \( \triangle EFG \) and \( \triangle TKZ \) are similar by comparing the ratios of their corresponding side lengths. Triangles are similar if their corresponding sides are proportional, meaning that the ratios of corresponding side lengths are equal.

The sides given are:
- For \( \triangle EFG \): \( EG = 3.25 \), \( EF = 2.5 \), and \( FG = 3 \).
- For \( \triangle TKZ \): \( TZ = 19.5 \), \( TK = 15 \), and \( KZ = 18 \).

We can set up and calculate the ratios of corresponding sides:

1. **Ratio of \( EG \) to \( TZ \):**
   \[
   \frac{EG}{TZ} = \frac{3.25}{19.5} = 0.1667
   \]

2. **Ratio of \( EF \) to \( TK \):**
   \[
   \frac{EF}{TK} = \frac{2.5}{15} = 0.1667
   \]

3. **Ratio of \( FG \) to \( KZ \):**
   \[
   \frac{FG}{KZ} = \frac{3}{18} = 0.1667
   \]

Since all three ratios are equal (\( 0.1667 \)), the sides are proportional. Therefore, the triangles \( \triangle EFG \) and \( \triangle TKZ \) are similar.

### Conclusion:
The correct statement is:
- **The triangles are similar because corresponding sides are proportional.**

Would you like further details on similarity in triangles or have any additional questions?

Here are five related questions:
1. What are the criteria for triangle similarity?
2. How do we calculate ratios to check for proportionality?
3. Can triangles be similar if only two sides are proportional?
4. What role do angles play in determining similarity of triangles?
5. How do we use similarity properties in solving real-world problems?

**Tip:** When comparing triangles, ensure that corresponding sides (those opposite the same angles) are used to maintain accuracy in your calculations.

Observe △EFG and △TKZ. Which statement below is valid?

Learn how to determine the similarity of triangles △EFG and △TKZ by comparing the ratios of their corresponding sides. This problem involves geometry concepts, including proportionality and the Triangle Similarity Theorem (SSS). Suitable for students in Grades 8-10.

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