A median and an altitude of an obtuse-angled triangle lie outside the triangle. It is true ?

Answer

To determine whether the statement "A median and an altitude of an obtuse-angled triangle lie outside the triangle" is true or false, we can analyze the properties of medians and altitudes in obtuse-angled triangles step by step.

### Step-by-Step Solution:

1. **Understanding the Obtuse-Angled Triangle**:
- An obtuse-angled triangle has one angle that is greater than 90 degrees. Let’s denote the triangle as \( \triangle ABC \) where \( \angle A \) is the obtuse angle.

2. **Defining the Median**:
- A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. For example, if we draw the median from vertex \( A \) to the midpoint \( D \) of side \( BC \), this median will always lie inside the triangle.

3. **Defining the Altitude**:
- An altitude of a triangle is a perpendicular line segment from a vertex to the line containing the opposite side. For instance, if we draw the altitude from vertex \( A \) to side \( BC \), it must meet side \( BC \) at a right angle (90 degrees).

4. **Analyzing the Altitude in an Obtuse Triangle**:
- In the case of an obtuse triangle, the altitude from the vertex opposite the obtuse angle (vertex \( A \)) will not meet side \( BC \) at a point within the triangle. Instead, it will extend outside the triangle to meet side \( BC \) at a right angle.

5. **Conclusion**:
- Based on the definitions and properties discussed:
- The median from vertex \( A \) to side \( BC \) lies inside the triangle.
- The altitude from vertex \( A \) to side \( BC \) lies outside the triangle.
- Therefore, the statement that "A median and an altitude of an obtuse-angled triangle lie outside the triangle" is **false**.

### Final Answer:
The statement is **false**.