Question

The centroid is the intersection of the _______ in a triangle.

Answer 1

In a triangle, the intersection, or precisely the concurrency, of the 3 perpendicular bisectors of the 3 sides is the circumcenter, the center of the circumscribed circle that passes 3 vertices of the triangle.

The intersection of 3 angle bisectors is the incenter, the center of the inscribed circle that is tangent internally to 3 sides.

The intersection of 3 altitude is the orthocenter. (From the Greek orthos means "straight". In mathematics, ortho implies perpendicular.)

Last but not least, the intersection of 3 medians, the segment that connects a vertex and the midpoint of its opposite side is the centroid of the triangle. The distance from the vertex to the centroid is 2/3 the length of the median.

We call it centroid because it is actually the "center" of the triangle. If we cut a piece of triangular cardboard and precisely locate the centroid, with a sharp point stick, and under no-wind situation, the triangle will level horizontally on the stick.

Answer 2

the centroid is the intersection of (medians)