The goal of this lesson is to use segment partitioning logic to prove that the medians of a triangle intersect in a single point.

Students begin by finding midpoints of the sides of triangles, and they learn that medians are segments that connect a triangle vertex to the midpoint of the opposite side. Next, they find points that partition the medians of a triangle in a ratio, observing in the process that the 3 medians of the triangle intersect in a single point. Finally, students work in groups to construct a viable argument that proves the medians of any triangle intersect at that partition point (MP3). While the intersection point of the medians isn’t given the formal name centroid in this lesson, it may be helpful to use that term.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.