Triangle Centers

using Geometers Sketchpad

Geometry Common Core PD Summer 2013

The following tasks show how to find various triangle centers using Geometer's Sketchpad

Centroid

Finding the intersection of the medians

Construct the triangle, construct the midpoints on the segments, construct segments connecting the midpoints to the vertices.


Incenter

Finding the intersection of the angle bisectors

Construct the triangle, construct the angle bisectors, find the point of intersection, construct a perpendicular with the point of intersection and a side, construct a segment using the intersection point of the angle bisectors and the perpendicular with the side (this is the radius), then finally construct the circle.


Circumcenter

Finding the intersection of the perpendicular bisectors

Construct a triangle, construct the midpoints, construct perpendicular lines using the midpoints, find the point of intersection, construct a circle using that point and one of the vertices of the triangle.


Orthocenter

Finding the intersection of the altitudes

Euler Line

What three special triangle centers lie on the same line no matter how you change the length of the sides of the triangle?