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