Assignment 4
Centroid of a triangle

This activity is designed to help students explore the properties of the centroid of a triangle using Geometer Sketch Pad.  This activity assumes students already have basic familiarity with GSP. 

The centroid of a triangle is the common intersection of the three medians. Follow the instructions below to construct the centroid of a triangle.

1. Open Geometer Sketch Pad.

2. Open a new sketch. 

3. Construct a triangle.  Once you've constructed the triangle, manipulate the vertices to create an acute triangle. 

5. Using your knowledge of segment bisection, bisect each side of the triangle to find the midpoint. 

6.  Join each midpoint to the vertex of the triangle opposite that midpoint.  The three medians created should intersect in one point.  Mark that point. 

Using your construction, answer the following questions on a seperate sheet of paper:

1. Each median divides the triangle into two halves.  How many "half triangles" are there in your picture? 

2. Measure the area of these "half triangles" by highlighting their vertices, constructing the triangle interior, and measuring the area.  What do you notice about the area measure? 

3. Now move one of the vertexes of your triangle.  What happens the the area measures? 

4. Make a conclusion about the median of a triangle.

5. Now measure the length of each median. 

6. Also measure the length from each vertex of the triangle to the centroid. 

7. What do you notice about the relationship between this number and the length of the median? 

Summary of Findings

The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). Each median divides the triangle into two equal pieces.  The centroid divides each of the medians in the ratio 2:1.  That is, the distance from any vertex of a triangle to the centroid, is two thirds the distance of the median emanating from that vertex. 

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