ICT student textbook/Exploring symmetry with Geogebra

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Exploring symmetry with Geogebra
In this activity, you will explore lines of symmetry, reflection and rotation of objects.

Objectives

1. Understanding rotation and reflection of geometric constructions
2. Reflecting objects and drawing lines of symmetry
3. Identifying lines of symmetry in given shapes visually
4. Recognizing symmetric and non-symmetric objects

What prior skills are assumed

1. Familiarity with the Geogebra application and tool bar
2. Able to create different Geogebra sketches using the various functionalities - line, line segment, measurement of angles, measurement of segments, drawing polygons

What resources do you need

1. Computer lab with projection equipment
2. Handout for Ubuntu
3. Handout for LibreOffice Writer
4. Handout for Geogebra
5. Geogebra files
6. Handout for screenshot

What digital skills will you learn

1. Creating Geogebra files to explore mathematical concepts
2. Inserting screenshots of Geogebra sketches in a text document and summarizing the mathematics investigation

Description of activity with detailed steps

Teacher led activity

Part 1- Locating and drawing lines of symmetry

Look at the following pictures with your teacher. Identify how many lines of symmetry are there.

• Figures with symmetry
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Your teacher will demonstrate the following:

1. How to insert an image in Geogebra
2. How to draw lines of symmetry to visually inspect symmetry?

Part 2 - Exploring ideas with symmetry with rotating and reflecting objects, in 2D and 3D

Your teacher will demonstrate the following to you in a Geogebra file:

1. Drawing a line and rotating it
2. Drawing a line segment and rotating it
3. Creating reflections of objects
4. Rotating polygons and creating new figures

See Geogebra handout for how to rotate objects. Your teacher may also introduce 3D visualization using Geogebra.

Student activities

Part 1 - Locating and drawing lines of symmetry

1. You can insert the images discussed with your teacher and draw the lines of symmetry
2. In the previous activity on Drawing with Geogebra, you had made several geometric sketches. Open those sketches and examine the axes of symmetry in those figures.

Part 2 - Exploring symmetry with reflection and rotation

1. Draw polygon shapes and rotate and reflect the polygon along a line or along a point. Explore what shapes you can produce.
2. Use the regular polygon tool and rotate around a point to see what shapes are produced.

Portfolio

1. Your Geogebra sketches will be part of the portfolio.