altitude of a triangle


Definition of Altitude of a Triangle

  • Altitude of a Triangle is the perpendicular distance from any of its vertices to the opposite side. (This opposite side of the vertex is called the base of the altitude.)

More about Altitude of a Triangle

  • As a triangle has 3 vertices, it has 3 altitudes.
  • Altitudes can be used to find the area of the triangle.

Example of Altitude of a Triangle

  • In the triangle ABC, AD is the perpendicular distance drawn from vertex A to the side BC. So, AD is the altitude of the triangle.

Solved Example on Altitude of a Triangle

Which of the figures shows an altitude of the triangle drawn?

Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. none of these
Correct Answer: C
Solution:
Step 1: Altitude of a triangle is the perpendicular distance from one of its vertices to its opposite side.
Step 2: The line drawn in Figure 3 from D to EF shows the perpendicular distance between D and EF.
Step 3: So, Figure 3 shows an altitude of the triangle drawn.

Related Terms for Altitude of a Triangle

  • Altitude
  • Base (of a Polygon)
  • Distance
  • Vertex