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Activity Overview

In this activity, students examine the location of the circumcenter and incenter for different triangles.

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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
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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
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After the Activity

Review student results:

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