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The problem asks about the similarity between quadrilaterals \(KLMN\) and \(WXYZ\), and it provides four answer choices to determine which statement is true based on their similarity properties.

### Key Points for Similarity:
1. **Corresponding angles** in similar figures are **congruent**.
2. **Corresponding sides** in similar figures are **proportional**.

We will evaluate each statement one by one:

- **Option A: \( \frac{KL}{WX} = \frac{WZ}{KN} \)**
  - This involves a proportion of sides, but the pairing is incorrect. The side \(KL\) corresponds to side \(WZ\), and \(KN\) corresponds to \(WX\). Therefore, this statement is **false**.

- **Option B: \( \angle NKL \) is congruent to \( \angle ZWX \)**
  - This compares the angles in the two similar quadrilaterals. Since corresponding angles in similar shapes are congruent, and \( \angle NKL \) corresponds to \( \angle ZWX \), this statement is **true**.

- **Option C: \( \frac{KL}{YZ} = \frac{LM}{ZW} \)**
  - This compares sides of the quadrilaterals, but the side \(KL\) should correspond to side \(WZ\), not \(YZ\). Thus, this statement is **false**.

- **Option D: \( \angle NKL \) is congruent to \( \angle XYZ \)**
  - This compares angles, but \( \angle NKL \) corresponds to \( \angle ZWX \), not \( \angle XYZ \). Therefore, this statement is **false**.

### Correct Answer:
The correct statement is **B: \( \angle NKL \) is congruent to \( \angle ZWX \)**, as corresponding angles in similar figures are congruent.

Would you like more details or clarification?

Here are some related questions you can explore:
1. How do you determine corresponding sides in similar quadrilaterals?
2. Why do corresponding angles remain congruent in similar figures?
3. How can side ratios help in identifying similarity between two polygons?
4. What is the role of proportionality in determining similarity?
5. How would you find the missing side length in a similar figure using proportionality?

**Tip:** Always match corresponding vertices and sides carefully when working with similar figures to ensure accuracy in your comparisons.

Quadrilateral KLMN is similar to quadrilateral WXYZ. Which statement is true?

Analyze the similarity between quadrilaterals KLMN and WXYZ by evaluating corresponding angles and proportions. Learn how to determine the true statement in this geometry problem, ideal for students in Grades 9-10.

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