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Median of a Triangle: Definition & Formula

Median of a Triangle: Definition & Formula
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  • 0:01 Median of a Triangle
  • 0:55 Properties
  • 1:34 Formulas
  • 2:40 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, we will look at the definition and properties of a median of a triangle. We will also look at three different formulas to find the length of a median in a triangle.

Median of a Triangle

A median of a triangle is a line segment that goes from one of a triangle's three vertexes to the midpoint of the opposite side. Because a triangle has three vertexes, it also has three medians. The three medians always meet at one point, and this point is called the centroid.

Let's clarify some things about the median of a triangle. A line segment is a part of a line that is defined by two end points. In this diagram, median Ma is bisecting side CB of the triangle. Median Ma is a line segment because it is part of a line that is defined by two end points. The end points are vertex A and the midpoint of side CB.

The vertexes of a triangle are simply its three points. In this diagram, the vertexes are labeled A, B, and C.

Properties

The three medians of a triangle will always meet at one point in the center of a triangle. As mentioned before, this point is the centroid. If one median is drawn, we can see that it forms two triangles within the bigger triangle. Both of these triangles are of equal size and area.

If three medians are drawn, we can see that they form six triangles, all with the same area but with different shapes. If the triangle is equilateral, where all sides are equal, all medians will be of equal length. If the triangle is isosceles, where two sides are equal, the medians extending from the two equal angles will be equal in length.

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