Exploring Centers of Triangles

Assignment 4

By Amber Candela


Let's Explore Triangles!

Using the explorations and Geometer's Sketchpad, explore properties of triangles.

Explorations were adapted from T³ Geometry Professional Development Confernce



In order to complete the investigations, you should know the following definitions

Altitude of a Triangle

Median of Triangle

Angle Bisector

Perpendicular Bisector

Link to Geometer's Skecthpad

Exploration 1

Which of the three segments (altitude, median or angle bisector) will divide the triangle into two equal areas?

Exploration 2

Draw triangle ABC and construct an angle bisector of angle ABC.

Exploration 3

Draw and label Triangle ABC and construct the midpoints of the three sides of the triangle

Exploration 4

Construct triangle ABC and construct the perpendicular bisectors of each side.

Exploration 4

Construct triangle ABC and construct the three altitudes

Exploration 5

Construct triangle ABC and bisect each of its three angles

Exploration 6

Construct triangle ABC

Triangle Centers Script Tools

Circumcenter: The intersection of the perpendicular bisectors of the sides.

Circumcenter Script Tool

Orthocenter: The intersection of the altitudes of the triangle

Orthocenter Script Tool

Incenter: The intersection of the angle bisectors

Incenter Script Tool

Centroid: The intersection of the medians

Centroid Script Tool