The centroid of a triangle is the common intersection of three medians.
A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.
For example in triangle ABC, D is the midpoint of the side BC. So AD is a median of the triangle.
The three medians of a triangle are concurrent. The point of concurrency is called the centroid.
Will the median always fall inside the triangle? Lets look at a three triangles.
If you have GSP then click here for an animation of the centroid of a triangle.
The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
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