Marking 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

Introduce medians of a triangle

Estimated Time

30 minutes.

Prerequisites/Instructions, prior preparations, if any

Triangle basics should have been covered.

Materials/ Resources needed

Non digital: Wax paper, pencil and ruler.

Process (How to do the activity)

1. On the piece of wax paper, use your pencil and ruler to draw a triangle.
2. Draw different types of triangles: Acute, Obtuse, or Right angled triangle.
3. Choose 1 side of your triangle. Fold your paper so that the endpoints of the side you’ve chosen are overlapping. Make a very small crease through the side of the triangle. This is the midpoint of the side.
4. Fold a crease in the triangle from this midpoint to the opposite vertex. You have now constructed the MEDIAN of one side of the triangle.
5. Use the same process to construct a median for the other two sides of the triangle.
6. What do you notice about their intersection point? The intersection point is called the centroid.

• Developmental Questions:

1. Where does the median lie in case of acute, obtuse and right triangles ?
2. Identify the centroid.
3. Into how many parts does the centriod divide the median ?
4. Compare your triangle and results to your partners.
5. Is centriod exactly in the middle of the median ?

• Evaluation:

1. Where exactly does the centroid lie on each median ?

• Question Corner

1. What is the position of the centroid in different types of triangles?