Constructing triangle centers

Review and picture of how to construct the following centers:

Orthocenter (H)

Centroid (G)

Circumcenter (C)

Incenter (I)

The following picture depicts the triangle centers with the lines of construction. Click here for a GSP script to view the construction of the triangle centers. Click here to open a GSP construction to manipulate the triangle centers.

 

 

The following depicts the centers withouth the construction lines.

 

 

Notice, by measuring the lengths of the sides of the triangles, that the centers are at the same point when the triangle is an equilateral triangle. Click here to open a GSP construction of the centers of the triangles to experiement with the centers yourself.