What does a mid segment of a triangle connect?

The mid segment of a triangle connects the midpoints of two sides. By definition, a mid segment is a line segment that joins the midpoints of two sides of a triangle. This segment has important properties; it is parallel to the third side and is half the length of that side. This relationship is particularly useful in various geometric proofs and problems, as it helps in establishing similarity between triangles or in calculating distances within the triangle.

To understand why the other options do not apply: connecting the endpoints of one side does not define a mid segment; rather, it merely refers to that side itself. The centroid and orthocenter are specific points related to the triangle but do not bear any connection to the mid segment's definition. Lastly, connecting all three vertices of the triangle refers to the triangle itself and does not describe a mid segment, which strictly pertains to the midpoints of only two sides. Thus, the correct understanding of a mid segment is fundamentally about connecting the midpoints of two sides of the triangle.