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The question asks which term describes **PS** in the context of triangle **PQR**, where point **S** lies on side **QR**, and **PS** is perpendicular to **QR**.

Here’s an analysis of the options:

- **A. Median**: A median connects a vertex to the midpoint of the opposite side. The problem doesn't indicate that **S** is the midpoint of **QR**, so this is unlikely to be correct.
  
- **B. Altitude**: An altitude is a line from a vertex perpendicular to the opposite side. Since **PS** is perpendicular to **QR**, this matches the definition of an altitude.
  
- **C. Angle bisector**: An angle bisector divides an angle into two equal parts, and nothing in the question suggests that **PS** bisects an angle.

- **D. Perpendicular bisector**: A perpendicular bisector not only forms a 90-degree angle with a side but also divides it into two equal parts. The question does not specify that **S** is the midpoint, so this doesn’t seem to apply.

Thus, the correct answer is **B. Altitude**.

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. What is the difference between an altitude and a median in a triangle?
2. How do you construct the altitude in any given triangle?
3. Can a line segment be both an altitude and a perpendicular bisector?
4. How does the position of the altitude change in different types of triangles (acute, right, obtuse)?
5. Why is it important to know the properties of triangle bisectors, altitudes, and medians?

**Tip:** In geometry, identifying key properties like perpendicularity and midpoint helps differentiate between similar terms like altitude and perpendicular bisector.

In triangle PQR, point S lies on QR. If PS is perpendicular to QR, which term describes PS?

Understand how to identify the altitude in triangle PQR where PS is perpendicular to QR. This problem focuses on key geometric concepts, including perpendicularity and the definition of altitudes in triangles. Suitable for students in Grades 7-9.

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