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To solve for \( k \), we need to use the property of similarity between triangles \( XYZ \) and \( ABC \). Since the triangles are similar, their corresponding sides are proportional. This means we can set up a proportion between the sides of \( XYZ \) and the corresponding sides of \( ABC \).

### Given:
- In \( \triangle XYZ \):
  - \( XZ = 3 \)
  - \( ZY = 6 \)
  - \( XY = 7 \)
  
- In \( \triangle ABC \):
  - \( AC = 4.5 \)
  - \( BC = 9 \)
  - \( AB = k \) (the value we want to find)

### Steps to Solve
1. **Set up the proportion for corresponding sides.** Since \( \triangle XYZ \sim \triangle ABC \), we can write:
   \[
   \frac{XZ}{AC} = \frac{ZY}{BC} = \frac{XY}{AB}
   \]

2. **Choose a pair of sides to solve for \( k \).**
   We’ll use the proportion involving \( XY \) and \( AB \), so:
   \[
   \frac{XY}{AB} = \frac{BC}{ZY}
   \]

3.

Triangle XYZ is similar to triangle ABC. Solve for k.

Learn how to solve for k in similar triangles XYZ and ABC using proportional sides. This solution demonstrates step-by-step application of the Triangle Similarity Theorem and proportion formulas. Suitable for students in Grades 8-10.

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