The students will find the circumcenter by constructing perpendicular bisectors of the sides of a triangle. They will also find the centroid by constructing the medians of a triangle and discover that the centroid is 2/3 of the distance from each vertex along each median.
Before the Activity
The students will need a copy of the Constructing a Centroid handout.
During the Activity
The students will estimate the location of the point that is equidistant from three given points. Then they will construct the perpendicular bisectors of the sides of the triangle to find the circumcenter and then construct the circle centered at the circumcenter that passes through the three points on the circle.
For the next problem the students will need the Constructing a Centroid handout to construct the medians of a triangle and find the centroid. The students will then discover that the centroid is 2/3 of the length of the median away from each vertex, by creating a calculation with a formula.