What is the altitude of a triangle?

The altitude of a triangle is defined as a line segment drawn from one vertex of the triangle that extends perpendicularly to the opposite side. This perpendicular distance represents the shortest path from the vertex to the line containing the opposite side, and it is crucial because it helps in calculating the area of the triangle. The area can be computed by using the formula: Area = (base × height) / 2, where the height refers to the length of the altitude. This concept is central in understanding triangle geometry and is applicable across all types of triangles, whether they are acute, right, or obtuse.

Understanding this definition allows students to apply the concept of altitude in various mathematical contexts, such as geometry problems involving area calculations, and also enhances their ability to visualize and analyze triangles in a more comprehensive way.