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The problem involves a triangle \( \triangle STU \) with a parallel segment \( ST \parallel VW \). We are given:

- \( US = 33 \)
- \( UV = 21 \)
- \( ST = 44 \)

The goal is to find the length of \( VW \).

Since \( ST \parallel VW \), we can apply the properties of similar triangles. Triangles \( \triangle STU \) and \( \triangle VWU \) are similar because of the parallel lines. Therefore, the sides of these triangles are proportional.

The proportionality is given by:

\[
\frac{VW}{ST} = \frac{UV}{US}
\]

Substitute the known values:

\[
\frac{VW}{44} = \frac{21}{33}
\]

Now, solve for \( VW \):

\[
VW = 44 \times \frac{21}{33}
\]

Let me calculate that.The length of \( VW \) is \( 28 \) units.

Do you want further details or have any questions?

Here are 5 related questions for practice:
1. If \( UT = 50 \), what would be the length of \( UW \)?
2. How would the result change if \( UV \) were increased to 25?
3. Can you derive a general formula for similar triangles when one side is parallel to the other?
4. How do parallel lines guarantee similarity in triangles?
5. What role does the Triangle Proportionality Theorem play in this problem?

**Tip:** Whenever you see parallel lines in geometry, check for possible similar triangles—it often simplifies problems through proportions.

Find the length of segment VW in a triangle where ST is parallel to VW and given US = 33, UV = 21, and ST = 44.

Explore how to find the length of segment VW in a triangle where ST is parallel to VW using properties of similar triangles. The problem uses given measurements US = 33, UV = 21, and ST = 44, demonstrating the application of the Triangle Proportionality Theorem. Suitable for high school geometry students.

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