Given that LP is a median of the `DeltaLMN`, explain where the point P lies.

Answer

To solve the question of where point P lies when LP is a median of triangle LMN, we can follow these steps:

### Step-by-Step Solution:

1. **Draw Triangle LMN**:
- Begin by sketching triangle LMN. Label the vertices as L, M, and N.

2. **Identify the Median**:
- A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. In this case, we are considering median LP, where L is one vertex of the triangle.

3. **Locate Midpoint of Side MN**:
- To find point P, we need to determine the midpoint of side MN. Let's denote the midpoint of MN as point P.

4. **Draw the Median**:
- Draw a line segment from vertex L to point P (the midpoint of MN). This line segment is the median LP.

5. **Understand the Property of the Median**:
- By definition, a median divides the opposite side (MN) into two equal segments. Therefore, we have:
- NP = PM
- This means that point P is equidistant from points N and M.

6. **Conclusion about the Position of P**:
- Since point P is the midpoint of side MN, it lies on line segment MN. Hence, point P is located on the line segment connecting points M and N.

### Final Statement:
- Therefore, point P lies on side MN of triangle LMN.

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