Altitude of a triangle is a line segment through a vertex and perpendicular to forming a right angle.

What is an Altitude of a Triangle?
An altitude of a triangle is a crucial concept in geometry. It is defined as the perpendicular segment from a vertex of the triangle to the line containing the opposite side.
Key Characteristics of Altitude:
- Definition: The altitude connects a vertex to the opposite side, forming a right angle with that side.
- Multiple Altitudes: Each triangle has three altitudes, one from each vertex.
- Intersection Point: The three altitudes intersect at a point known as the orthocenter of the triangle.
Types of Triangles and Their Altitudes:
- Acute Triangle: All three altitudes lie inside the triangle.
- Right Triangle: One altitude is along one of the legs, while the other two lie within the triangle.
- Obtuse Triangle: One altitude falls outside the triangle, while the other two remain inside.
Importance of Altitude:
- Area Calculation: The altitude is vital for calculating the area of a triangle using the formula: Area = 1/2 * base * height (where height is the altitude).
- Geometric Properties: Understanding altitudes aids in solving various geometric problems and proofs.
- Real-World Applications: Altitudes are used in fields such as architecture, engineering, and navigation, where precise measurements are essential.
In summary, the altitude is a fundamental element in understanding triangles, influencing both theoretical and practical applications across different fields.