Triangle Center Applet
Use the applet to determine the difference in triangle centers.
The center of a triangle is a point that relates all vertices or sides to one another. There are four triangle centers: orthocenter, centroid, incenter, and circumcenter.
Explore the four centers of a triangle by creating the various centers in the following steps and using the pre-constructed centers to identify the differences between them. Recall what you know about altitudes, angle bisectors, perpendicular bisectors, and medians as you work. Clear each of the centers you create after each step so you have a clear spot to construct the next triangle center.
- Construct the altitudes of the triangle by checking the box. Before doing so, take a moment to recall: What is an altitude? How is it different from other types of triangle segments? Check the triangle center boxes to determine the center that is created by the intersection of the altitudes.
- Construct the angle bisectors of the triangle by checking the box. Before doing so, recall: What is an angle bisector? Check the triangle center boxes to determine the center that is created by the intersection of the angle bisectors.
- Construct the perpendicular bisectors of the triangle by checking the box. Before doing so, recall: What is a perpendicular bisector? How does it differ from an altitude? Check the triangle center boxes to determine the center that is created by the intersection of the perpendicular bisectors.
- Construct the medians of the triangle by checking the box. Before doing so, recall: What is a median? Check the triangle center boxes to determine the center that is created by the intersection of the medians.
- Do any of the centers always stay inside the triangle? Which ones?
- Are the centers ever the same?
- What happens when the triangle is equilateral? Right? Isosceles?