Activities

• • • Subject Area

• Math: Geometry: Triangles

• Author 9-12

60 Minutes

• Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• Software

Cabri Geometry™
TI Connect™

• Accessories

TI Connectivity Cable

• Other Materials
This is Activity 7 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

Centroid and Orthocenter

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.

• 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