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Incenter of a Triangle

Lesson Summary:Students will discover the properties of an incenter of a triangle. The incenter is found by

constructing the angle bisectors of the angles of a triangle.

Key Words:

incenter, incircle, inscribed, angle bisectors, concurrency

Background Knowledge:Students should be familiar with the tools in Geometry software. Students also shouldunderstand the meanings of inscribed and angle bisectors.

NCTM Standards:

(4) Geometry; Standard 7 Geometry from a synthetic perspective

Learning Objectives:1. To apply understanding of angle bisector into creating the incenter of a

triangle

2. To understand the basic characteristics of the incenter and incircle of atriangle

Materials:Cabri II

One copy of the lab worksheet per person

Suggested Procedures:

Organize students into groups of 2-3 Ask students to define the center of a triangle. Discuss how to draw a circle

around the triangle and inside the triangle.

Have students complete the lab worksheet.

Project AMP Dr. Antonio Quesada Director, Project AMP

8/9/2019 In Center

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8/9/2019 In Center

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7. Move the vertices A, B, or C. What do you observe?

8. Construct a circle with center point I and radius as one of the perpendicularsegments. (use circle tool)

(This circle is called the incircle of the triangle!)

9. Move points A, B, or C again. What do you observe about the circle?

11. Is the incircle tangent to the three sides? Why?

12 What observations can you make about the incenter of a triangle?

* If you are not familiar with Cabris tools, press F1 on the keyboard. A help

menu for each tool selected will appear on the bottom of the screen.

Project AMP Dr. Antonio Quesada Director, Project AMP

8/9/2019 In Center

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Journal Activity

Incenter of a Triangle

1. What was your favorite thing about this activity?

2. What was the most challenging thing?

3. What did you gain the most confidence about through completing thislesson?

4. Where do you possibly see yourself using this knowledge in the future?

Project AMP Dr. Antonio Quesada Director, Project AMP