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 6 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

## Circumcenter and Incenter

#### Activity Overview

In this activity, students examine the location of the circumcenter and incenter 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 23 - 25 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 perpendicular bisectors of each side and observe that all perpendicular bisectors intersect in only one point
• Determine the location of the circumcenter (the intersection point of the perpendicular bisectors)
• Note that when the triangle is acute, the circumcenter lies inside the circle
• Alter the triangle to create an obtuse triangle
• Observe that when the triangle is obtuse, the circumcenter lies outside the circle
• Alter the triangle to create a right triangle
• Note that if a triangle is right, the circumcenter lies on the triangle

• Create an acute triangle and construct angle bisectors of each angle
• Observe that the angle bisectors of a triangle have only one point of intersection called the incenter
• Determine the location of the incenter
• Note that when the triangle is acute, the incenter lies inside the circle
• Alter the triangle to create an obtuse triangle
• Determine the location of the incenter
• Alter the triangle to create a right triangle
• Determine the location of the incenter
• Note that for acute triangles, obtuse triangles, and right triangles, the incenter lies inside the triangle
• #### After the Activity

Review student results:

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