Geometry — Medians of the Triangle

About this lesson

This unit teaches the concept of medians in a triangle, including their definition as line segments from a vertex to the midpoint of the opposite side, and the fact that the three medians are concurrent at a point called the centroid (also known as the geometric center or equilibrium point). It covers the property that the centroid divides each median in the ratio 2:1 from the vertex, and the corollary that a point dividing a median in that ratio is the centroid. The unit also presents a theorem about right-angled triangles: the median drawn from the right angle vertex equals half the length of the hypotenuse, along with its converse. Examples and exercises involve finding lengths of medians, segments, and sides using these properties, often combined with the Pythagorean theorem. Real-life contexts include drones with three arms, a triangular glass tabletop needing balance, and a triangular garden with median paths. By the end, students should be able to identify medians and centroids, apply the ratio property, use the right-triangle median theorem and its converse, and solve related problems.