Circumcenter and Incenter

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Triangles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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.

Follow the Activity procedures:

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

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Triangles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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Circumcenter and Incenter

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Circumcenter and Incenter

Before the Activity Files

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

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