Use the applet to determine the difference in triangle centers.

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. Note that you should clear each of the centers you create after each step, so you have a clear spot to construct the next triangle center.[br]1. Construct the altitudes of the triangle by checking the box. An altitude is the line segment from a vertex perpendicular to the line containing the opposite side. Check the triangle center boxes to determine the center that is created by the intersection of the altitudes.[br]2. Construct the angle bisectors of the triangle by checking the box. Check the triangle center boxes to determine the center that is created by the intersection of the angle bisectors.[br]3. Construct the perpendicular bisectors of the triangle by checking the box. Check the triangle center boxes to determine the center that is created by the intersection of the perpendicular bisectors.[br]4. Construct the medians of the triangle by checking the box. A median is the line that connects the vertices to the midpoints of the opposite side. Check the triangle center boxes to determine the center that is created by the intersection of the medians.[br][br]Once you have identified the different centers of the triangles, check all of the triangle center boxes. Adjust the vertices of the triangles and note some characteristics of each of the centers. [Do they stay within the triangle?, Are they ever the same?, etc.]