a triangle is a segment joining the midpoints of two sides of a triangle.

When three or more lines meet at a single point, they are said to be concurrent. In a triangle, the three medians, three perpendicular bisectors, three angle bisectors, and three altitudes are each concurrent.

The circumcenter of a triangle is the point where the three perpendicular bisectors meet. This point is the same distance from each of the three vertices of the triangles.

A median is a segment connecting any vertex of a triangle to the midpoint of the opposite side.

The centroid of a triangle is the point where the three medians meet. This point is the center of mass for the triangle. If you cut a triangle out of a piece of paper and put your pencil point at the centroid, you could balance the triangle.

An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.

The orthocenter of a triangle is the point where the three altitudes meet, making them concurrent.