See Constructing a perpendicular bisector of a line segment
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| After doing this | Your work should look like this |
|---|---|
| We start with a triangle PQR. | |
| First, we draw the median of the triangle through R | |
| 1. Construct the bisector of the line segment PQ. Label the midpoint of the line S.
See Constructing a perpendicular bisector of a line segment |
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| 2. Draw the median from the midpoint S to the opposite vertex R | |
| Next, we draw the second median of the triangle through P | |
| 3. In the same manner, construct T, the midpoint of the line segment QR. See Constructing a perpendicular bisector of a line segment | |
| 4. Draw the median from the midpoint T to the opposite vertex P | |
| (Optional step) Repeat for the third side. This will convince you that the three medians do in fact intersect at a single point. But two are enough to find that point. | |
| 5. Done. The point C where the two medians intersect is the centroid of the triangle PQR. | |