Education Technology

Centroid and Orthocenter

Published on 06/09/2008

Activity Overview

In this activity, students analyze the location of the centroid and orthocenter for different triangles.

Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 27 - 29 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Construct an acute triangle and label its vertices
  • Construct medians and notice that all medians intersect in a point, called the centroid
  • Determine the location of the centroid
  • Alter the triangle by dragging one of the vertices around the screen to create an obtuse triangle
  • Determine the location of the centroid
  • Alter the triangle to create a right triangle
  • Determine the location of the centroid
  • Note that for all triangles, the centroid lies inside the triangle


  • Create an acute angled triangle and construct its altitudes
  • Note that all altitudes of a triangle have only one point of intersection, called the orthocenter
  • Determine the location of the orthocenter
  • Identify that when the triangle is acute, the orthocenter lies inside the triangle
  • Alter the triangle to create an obtuse angle
  • Observe that when the triangle is obtuse, the orthocenter lies outside the triangle
  • Alter the triangle to create a right angle
  • Observe that the orthocenter lies on the triangle
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary