Medians and centroid of a triangle

The median of a triangle is the line segment that joins the vertex to the midpoint of the opposite side of the triangle. The three medians of a triangle are concurrent in a point that is called the centroid. There is a special relationship that involves the line segments when all of the three medians meet. The distance from each vertex to the centroid is two-thirds of the length of the entire median drawn from that vertex.

Objectives

To introduce medians of a triangle and their point of concurrence.

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Types of triangles, their medians and their constructions should have been covered.

Materials/ Resources needed

This geogebra file has been done by ITfC- Edu- Team

Process (How to do the activity)

1. The teacher can use this geogebra file to show how the position of centriod is constant in different triangles.

• Developmental Questions:

1. Which type of triangle is this ?
2. What is a median ?
3. How do you identify the midpoint of the side ?
4. Which is the point of concurrency of medians of the triangle ?
5. Identify the position in different triangles.

• Evaluation:

1. What is the position of centriod in different triangles ?

• Question Corner:

1. Why do you think the centriod always remains in the centre for every type of triangle ?
2. What does the centriod indicate ?
3. What are the practical applications of the centriod ?