A median of a triangle is a line segment from a vertex of the triangle to the midpoint of the side opposite that vertex. Because there are three vertices, there are of course three possible medians. One of the fascinating things about them is that no matter what shape the triangle, all three always intersect at a single point. This point is called the centroid of the triangle.

Properties

1. The fact that the three medians always meet at a single point is interesting in its own right
2. Each median divides the triangle into two smaller triangles which have the same area
3. The centroid (point where they meet) is the center of gravity of the triangle
4. The three medians divide the triangle into 6 smaller triangles that all have the same area, even though they may have different shapes.

Adjust the triangle above by dragging any vertex. Convince yourself that the three medians (gray lines) always intersect at a single point. You can also visually estimate that the area facts given above are true.

Try this

1. Make any triangle about 12 - 24" wide from cardboard. Make it as lop-sided and irregular as you can.
2. Draw a median on the cardboard triangle. Any one will do.
3. At the point where the median meets the side of the triangle make a small hole near the edge. Tie a string through it.
4. When you hold up the triangle by the string, the median line should be vertical - exactly in line with the string.(see figure below)
5. Why?

Related triangle topics

General

• Triangle definition
• Hypotenuse
• Triangle interior angles
• Triangle exterior angles
• Pythagorean Theorem
• A graphical proof of the Pythagorean Theorem
• Pythagorean triples
• Triangle circumcircle
• Triangle incircle
• Triangle medians
• Midsegment of a triangle
• Triangle inequality
• Side / angle relationship

Perimeter / Area

• Perimeter of a triangle
• Area of a triangle
• Heron's formula
• Area of an equilateral triangle
• Area by the "side angle side" method
• Area of a triangle with fixed perimeter

Triangle types

• Right triangle
• Isosceles triangle
• Scalene triangle
• Equilateral triangle
• Equiangular triangle
• Obtuse triangle
• Acute triangle
• 3-4-5 triangle
• 30-60-90 triangle
• 45-45-90 triangle

Triangle centers

• Incenter of a triangle
• Circumcenter of a triangle
• Centroid of a triangle
• Orthocenter of a triangle
• Euler line

Congruence and Similarity

• Congruent triangles

Solving triangles

• Solving the Triangle
• Law of sines
• Law of cosines

Triangle quizzes and exercises

• Triangle type quiz
• Ball Box problem
• How Many Triangles?
• Satellite Orbits