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### Course: Geometry (all content)>Unit 4

Lesson 6: Medians & centroids

# Triangle medians & centroids

The centroid of a triangle is the point at which the three medians intersect. To locate the centroid, draw each of the three medians (which connect the vertices of the triangle to the midpoints of the opposite sides). It is referred to as the "center of mass" or "balance point" of the triangle. Centroid divides medians in a ratio 2:3. Created by Sal Khan.

## Want to join the conversation?

• I did not get how the 3-d triangle he drew was different from the 1st one. And why is it simpler for the math to draw 3d shapes? just wondering.
• If you look at the 2D proof in the next video, you see that the math is much more complex. With the 3D, Sal is able to use two zeros in each coordinate, which simplifies the equations.
• What is a vertex?
(1 vote)
• A vertex is the point where two rays or lines meet
• is the median an angle bisector
• The definition of a median is the line segment from a vertex to the midpoint of the opposite side. It is also an angle bisector when the vertex is an angle in an equilateral triangle or the non-congruent angle of an isoceles triangle.
• when do we use a z axis?
• In 3D things or when working with objects or shapes that have depth length and width
• Are centroids only in triangles?
• I am actually not sure, but I think so. Try it out to see.
(1 vote)
• At . This proof seems to depend on the coordinates of the centroid being located at (a/3,b/3,c/3). I can't figure this out, and I don't like to take things on faith, especially in math. Can someone tell me why this is so or where I can find the answer?
• Each value is divided by 3 because that is the average. He summed all the coordinates for a, which were 3, and divided by that number, which is exactly what you do when you find an average: (a+0+0)/3. He did this for b and c and found the average values for each coordinate. This average value gives the centroid.
• At , what is Sal talking about? I don't understand what he is talking about?
• At that point of the video, Sal is drawing a three-dimensional triangle. He states that he is not making any assumptions of what type of triangle it is because if it were a equilateral or isosceles triangle, calculations might have been different.