Altitude in Geometry

In geometry, the term "altitude" refers to a perpendicular line segment drawn from a vertex of a triangle to the side opposite that vertex. This line segment represents the height of the triangle and can be used to calculate various properties of the triangle.

Calculating the Altitude

To calculate the altitude of a triangle, you can use the formula:

Altitude = (2 * Area of the triangle) / (Base of the triangle)

Where the area of the triangle is calculated using the formula:

Area = (1/2) * Base * Height

Using these formulas, you can find the altitude of the triangle by first calculating its area and base, and then plugging these values into the altitude formula.

Properties of Altitudes

Altitudes have several important properties in geometry:

1. Altitudes always intersect the opposite side of the triangle at a right angle, forming right triangles within the larger triangle.
2. The point of intersection between the altitudes (known as the orthocenter) is the center of the circumcircle of the triangle.
3. Altitudes can be used to calculate the area of a triangle using the formula mentioned above.

Study Guide

When studying altitudes in geometry, make sure to focus on the following key points:

• Understanding the definition of altitude as a perpendicular line segment from a vertex to the opposite side of a triangle.
• Knowing how to calculate the altitude of a triangle using the area and base.
• Recognizing the properties of altitudes, including their intersection at the orthocenter and their role in calculating triangle area.
• Practicing problems involving altitudes to solidify your understanding of the concept.

By mastering these concepts and properties, you can confidently work with altitudes in geometry and apply them to various problem-solving scenarios.