Altitude of a Triangle
• Definition:
The altitude of a triangle is a line segment from a vertex perpendicular to the opposite side (or its extension). It forms a right angle with the base of the triangle and is used to determine the height of the triangle.
• Finding Altitude:
To find the altitude of a triangle, you can use the formula:
Altitude = (2 * Area of the triangle) / Base
• Types of Altitudes:
1. **Perpendicular Bisector** - A line that goes through the midpoint of a side and is perpendicular to it.
2. **Angle Bisector** - A line that divides an angle into two equal angles and is perpendicular to the opposite side.
3. **Median** - A line that connects a vertex to the midpoint of the opposite side.
4. **Altitude** - A line that is perpendicular to the base from a vertex.
• Properties:
- Altitudes of a triangle intersect at a point called the orthocenter.
- The length of altitudes can vary depending on the type of triangle (acute, obtuse, or right).
- Altitudes can help calculate various properties of a triangle, such as area, perimeter, and angles.
In conclusion, the altitude of a triangle plays a crucial role in geometry by providing a way to measure the height of the triangle and determine its various properties. Understanding altitudes can help in solving geometric problems and analyzing the relationships between different parts of a triangle.