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# Introduction to Constructions with Geometer's Sketchpad

Lesson 8 of 13

## Objective: SWBAT use Geometer's Sketchpad to investigate geometric theorems.

#### Mini-Lesson

*10 min*

The purpose of this lesson is to familiarize students with the program Geometer's Sketchpad. Most of the lesson involves students exploring the program on their own. However, I usually give a short introduction with a few pointers.

I start off by having the students investigate the definition of a circle, which says, "A circle is the set of all points equidistant from one point called the center." Students start by constructing a circle. They label the center and change the name from "A" to "O." Next, students construct 5 different points on the circle and measure the distance between the points on the circle and the center. Students see that the distances are all the same. If the distances between the points are not the same, it may be that the points are not actually on the circle.

Students then connect each point on the circle to the center point to form a radius. They measure the length of each radii. Students see that the length of a radius is the same as the distance between a point on the circle and the center point. The concept that the distance between two points is the same as the length of the segment connecting the two points will come up again in later lessons.

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#### Activity

*20 min*

Students will work on three constructions and answer questions about those constructions. The constructions they perform are the same as ones they performed with pencil and paper. This allows to learn how to use the program by doing something they already know how to do and to see the same concept in slightly different ways.

As I circulate, I offer minimal help. When students ask me how to do something, I instruct them to try on their own or to ask other students. Students need to learn for themselves how to do things and then program is so user-friendly that they are able to figure it out on their own. Since this is the first activity with Geometer's Sketchpad, I do not grade the work. I have the students e-mail me their work and hand in the sheet so I can look at it and ensure they know what to do.

Students who finish the constructions can explore the program more. I usually keep self-guided investigations for student to work on. These can be found on the website www.dynamicgeometry.com.

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#### Summary

*5 min*

Since my students use laptops, I usually need some time at the end of class to collect them. While I am collecting the laptops, I have the students answer the following questions.

**Exit Ticket:** List 3 things you can do with Geometer's Sketchpad. List 2 ways how Geometer's Sketchpad differs from paper and pencil constructions. List 1 new thing you learned today.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: What is Geometry?
- LESSON 2: Geometric Terms
- LESSON 3: What are Geometric Constructions?
- LESSON 4: Bisecting Angles
- LESSON 5: Constructing Parallel Lines
- LESSON 6: Constructing Triangles
- LESSON 7: Constructing Inscribed Regular Triangles, Quadrilaterals and Hexagons
- LESSON 8: Introduction to Constructions with Geometer's Sketchpad
- LESSON 9: Constructing Quadrilaterals using Geometer's Sketchpad
- LESSON 10: Constructing Regular Polygons Inscribed in Circles using Geometer's Sketchpad
- LESSON 11: Geometric Construction Review
- LESSON 12: Geometric Constructions End of Unit Assessment
- LESSON 13: Geometric Constructions Assessment Error Analysis