Mastering the Centroid: Medians and Segment Ratios in Triangles

Miacademy & MiaPrep Learning Channel

This video provides a comprehensive geometry lesson focused on understanding the centroid of a triangle. The narrator, Justin, guides students through the fundamental concepts of medians—segments connecting a vertex to the midpoint of the opposite side—and explains how the intersection of these three medians forms the centroid. The video uses clear visual aids, including color-coded diagrams and tick marks, to illustrate these geometric properties. The core of the lesson explores the specific mathematical relationship created by the centroid. It details the 2:1 ratio property, explaining that the distance from the vertex to the centroid is always twice the distance from the centroid to the opposite side. The video also breaks this down into fractional parts, helping students visualize the segments as 1/3 and 2/3 of the entire median length. This conceptual framework is then applied to solving algebraic and numerical geometry problems. For educators, this video is an excellent resource for introducing or reinforcing triangle centers in a high school geometry curriculum. It is designed to be interactive, encouraging students to pause and take notes using color-coded pencils, and includes a "pause-and-try" example problem that scaffolds learning from simple identification to multi-step calculation. The lesson concludes by teasing a hands-on "pencil balance" activity, connecting the abstract geometric concept to the physical property of the center of gravity.