# Triangle Centers

## Geometry Common Core PD Summer 2013

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

## Finding the intersection of the medians

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

## 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.

## 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.

## 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?