Your teacher will tell you how to draw and label the medians of this triangle.

1. After the medians are drawn and labeled, measure all 6 segments inside the triangle using centimeters. What is the ratio of the 2 parts of each median?
2. Find the coordinates of the point that partitions segment in a ratio.
3. Find the coordinates of the point that partitions segment in a ratio.
4. Find the coordinates of the point that partitions segment in a ratio.

The goal is to prove that the medians of any triangle intersect at a point. Suppose the vertices of a triangle are and .

1. Each student in the group should choose 1 side of the triangle. If your group has four people, two can work together. Write an expression for the midpoint of the side you chose.
2. Each student in the group should choose a median. Write an expression for the point that partitions each median in a ratio from the vertex to the midpoint of the opposite side.
3. Compare the coordinates of the point you found to those of your groupmates. What do you notice?
4. Explain how these steps prove that the 3 medians of any triangle intersect at a single point.