a line joining the midpoints of two sides of a triangle.

The bottom of a pyramid is a mid-segment. 

When three or more lines meet at a single point

when telaphone wires cross they are concurrent

the point where the three perpendicular bisectors meet.

The middle of a triangle is the circumcenter.

segment connecting vertex of a triangle to the midpoint of the opposite side.

the top half of a pyramid is its median.

the point where the three medians meet.

The distance between a vertex of a triangle and the opposite side.

the distence between the top and bottom of a payramid is it altitude.

The point at which the three (possibly extended) altitudes of a triangle intersect

the center of a pyramid is it orthocenter