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

Lesson 6: Medians & centroids

# Dividing triangles with medians

Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well. Created by Sal Khan.

## Want to join the conversation?

• Can someone please explain the difference between a median, an angle bisector, and a perpendicular bisector? Thank you.
• Median - A line segment that joins the vertice of a triangle to the midpoint of opposite side.
Angle bisector - A line segment that divides an angle of a triangle into two equal angles.
Perpendicular bisector - A line segment that makes an angle of 90 deg (right angle) with the side of a triangle.

The common point where the medians intersect is the centroid.
The common point where the angle bisectors intersect is the incenter.
The common point where the perpendicular bisectors intersects is the circumcenter.
• Is there somewhere on this site where I can practice this information?
• You should talk to your geometry teacher or the geometry teacher at your school. (assuming you're in school.) They could probably put something together for you.
• What exactly is the difference between a median and a midsegment?
• Here is a diagram of a triangle ABC with D, E, and F representing the midpoints of the three sides. AF is a median (a line segment connecting one vertex to the midpoint of the opposite side), and DE is a midsegment (a line segment connecting the midpoints of two sides).
• Is there a proof that shows that the three medians of a triangle will all intersect at the centroid?
• If you draw a another line in between that passes through a point in between E and C. Do the triangles formed still have the same area?
• From the middle of EC up to B?

or to the point 1/3 of the way above F on line FB?
• How do we find the median and the centroid ratio from shapes with more than 3 sides (triangles)? is it possible to do it with an even number of sides? - I couldn't see how.
• These are special points and lines in triangles, some don't exist the same way in higher order polygons. Even if we could construct them, they wouldn't behave the same way (as in, they wouldn't be concurrent at one point).
• how do we know that BE is the height of BEC and BEA if neither of those triangles is a right triangle? The medians of a triangle aren't necessarily perpendicular bisectors of the sides, are they?
• The altitude, or height of a triangle is defined to be perpendicular to the base. Therefore, the heights are equal.