Lesson Plan. Important Lines in a Triangle – The Median

Objectives

By the end of the lesson, students will be able to:

Define the median of a triangle.
Identify the medians in a given triangle.
Draw the medians and locate the centroid (G).
Explore the relationship between the medians and the centroid using a GeoGebra animation.

Definition: a median of a triangle is the segment joining a vertex to the midpoint of the opposite side.

Properties:

The three medians are concurrent (they meet at one point).
The common point is called the centroid (G).
The centroid divides each median in the ratio 2:1, with the longer part from the vertex.

1. Introduction	Teacher shows a triangle and asks: “How can we divide it evenly?”	5 min
2. Announcing topic	“Today we’ll learn about medians and the centroid.”	2 min
3. New content	Explain definition, draw medians on board or GeoGebra.	10 min
4. Practice	Students draw triangle and medians, checking intersection point.	10 min
5. Digital activity (GeoGebra)	GeoGebra animation: dragging vertices to observe centroid movement.	10 min
6. Consolidation	Discussion: What is the ratio along the median?	8 min
7. Assessment	Short task: “Draw triangle ABC, mark midpoints, draw medians, and label centroid G.”	5 min

Methods: guided discussion, problem-solving, demonstration, practical activity.

Tools: board, ruler, set square, notebook, GeoGebra animation (centroid visualization).

Draw two triangles (isosceles and scalene) and draw their medians. What do you notice about the centroid’s position?