Centroid Mobile

What is the center of a triangle?

The center of a triangle is a very interesting topic in Geometry. Actually, there is not one but a number of different types of centers; the ones you will learn in this unit are the orthocenter, circumcenter, incenter and centroid.

TheCentroid of a triangle is the point at which the medians of the triangle meet. Since a median is a segment, and always in the interior of the triangle, the centroid is always inside the triangle as well.

In this project, we will explore the most interesting property of the centroid: it is also the center of balance, or center of gravity of the triangle!

Materials: 1 piece of cardstock, ruler, protractor/compass, scissors, metal “brad”, string, stick

1) Divide your piece of cardstock into 3 different triangles. Use the entire piece of cardstock. Cut out the triangles.

2) Construct all 3 medians in each triangle.

3) When you have completed your triangles, you will find that if you push the sharp point of a pencil slightly into the centroid, you can balance their triangle on this point.

4) Be creative! Design the back side of each triangle. Give your mobile a theme!

5) You can hang your triangle by pushing the metal tabs of a brad through the centroid of each triangle. If the tabs of the brad or point of the tack are then bent to make a small loop, you can hang a triangle from fishing line or string, and see that it balances on that point.

6) Use a wooden rod, metal rod, or stick to make a mobile combining all three or more of the triangles you created.

7) Tag your mobile with your names and theme.