https://file.aiquickdraw.com/mathbot/file/17272182143762msg565a.jpg

To prove that line \( SU \perp TV \), we need to show that the two lines are perpendicular, meaning they intersect at a right angle (90 degrees). 

From the diagram, we observe the following:

- The point \( W \) is the intersection point of the two lines \( SU \) and \( TV \).
- \( SU \) is a vertical line, passing through points \( S \), \( W \), and \( U \).
- \( TV \) is a horizontal line, passing through points \( T \), \( W \), and \( V \).
- The red marking on the diagram indicates that the angle formed between these two lines at point \( W \) is a right angle (90°).

### Formal Proof:
1. **Intersection Point**: The lines \( SU \) and \( TV \) intersect at the point \( W \).
   
2. **Vertical and Horizontal Lines**: 
   - \( SU \) is a vertical line, so all points on this line have the same \( x \)-coordinate.
   - \( TV \) is a horizontal line, so all points on this line have the same \( y \)-coordinate.
   
3. **Angle Between the Lines**:
   - The diagram shows a right angle (90°) formed at the intersection \( W \) between the two lines.
   - By definition, two lines are perpendicular if the angle between them is 90°.

4. **Conclusion**: Since the angle between \( SU \) and \( TV \) at \( W \) is 90°, we can conclude that \( SU \perp TV \).

Thus, the lines \( SU \) and \( TV \) are perpendicular.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is the definition of perpendicular lines?
2. How can the slope of perpendicular lines be determined algebraically?
3. What is the significance of the intersection point in defining perpendicularity?
4. Can two lines be perpendicular without forming a 90° angle visually? Why or why not?
5. How can we prove perpendicularity using coordinates?

**Tip:** When working with perpendicular lines, their slopes (in a coordinate plane) are negative reciprocals of each other (e.g., if the slope of one line is \( m \), the other line has a slope of \( -1/m \)).

This proof demonstrates how to prove that SU is perpendicular to TV using geometric principles, such as vertical and horizontal lines and the definition of a right angle. The problem is suitable for students in Grades 7-9.

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