Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Triangles

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.

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