1.30 Construct a Centroid
The point where a triangle's three medians intersect is called the centroid. A median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.
To construct the centroid, it is sufficient to find the intersection of two medians, since the third median will also pass through this point.
Construct a Centroid using MIDPOINT 
tool
Follow the steps below to construct the centroid.
tool
Follow the steps below to construct the centroid.
- Construct the midpoint of side AB. Click on and then on A and B. *Repeat this step with side AC.
- Construct a median on segment AB: Click on
to connect the midpoint of AB with point C. - Construct a median on segment AC. Click on to connect the midpoint of AC with point B.
- Mark the centroid (the point of intersection of the medians): Click on
and then click on each median.
Construct a Centroid using COMPASS 
tool
1) Construct the midpoint of side AB.
to connect the midpoint of AB with point C.
3) Construct a median on segment AC. Click on to connect the midpoint of AC with point B.
4) Mark the centroid (the point of intersection of the medians): Click on 
and then click on each median.
tool
1) Construct the midpoint of side AB.
- Construct a circle with radius AB centered on A. Click on and then on point A and point B. Then, click on point A again to center on point A.
- Construct a circle with radius AB centered on B. Click on and then on point A and point B. Then, click on point B again to center on point B.
- Mark the points of intersection of the two circles. Click on and then click on each circle.
- Construct a segment (perpendicular bisector) between the two points of intersection of the circles. Click on and then click on the two points of intersection.
- Construct the midpoint of side AB. Click on and then click on the perpendicular bisector segment and then click on side AB of the triangle.
- Hide the circles, segment, and points of intersection of the circles. Click on
and then on any part that you want to hide. *Be sure not to hide the original triangle or the midpoints of the sides of the triangles. - Repeat these steps with side AC.
to connect the midpoint of AB with point C.
3) Construct a median on segment AC. Click on to connect the midpoint of AC with point B.
4) Mark the centroid (the point of intersection of the medians): Click on and then click on each median.