Getting Started With Interactive Geometry Software

Transcription

1 Getting Started With Interactive Geometry Software Peter Johnston Wilder and Alison Parish

2 Published in 2007 by Association of Teacher of Mathematics Unit 7 Prime Industrial Park, Shaftesbury Street Derby DE23 8YB Telephone Fax admin@atm.org.uk 2007 Alison Parish and Peter Johnston Wilder Printed in England ISBN Copies may be purchased from the above address or This publication is in copyright. No reproduction of any part may take place without the written permission of the Association of Teachers of Mathematics.

3 Association of Teachers of Mathematics Getting Started with Interactive Geometry Software Contents Introduction page 1 1 Play 2 2 Euclid's Tools 8 3 Measurement Too Is 28 4 Transformation Tools 34 5 Locus Tools 38 is a freely available program downloadable from: ems/

4 INTRODUCTION This book is about learning to use a piece of software. It includes two kinds of activity: Tasks are detailed worked examples with step-by-step instructions for performing certain kinds of task, in which software ideas are demonstrated; Try this are more open activities in which you are invited to apply and explore these ideas for yourself. Before learning to use a piece of software, many people need to play, in order to develop an appreciation of what the software can do, and to get a sense of what they wish to achieve. Before you start this book, we recommend that you look at the website to get a sense of what interactive geometry can do. There are now many interactive geometry software packages available and these are demonstrated on the MathsNet website. All are based on similar underlying principles, and use the same basic toolkit for constructions. The Geometer's Sketchpad and Cabri Geometry 11 are those most commonly found in schools. Freeware versions on common use are and C.a.R. (Compass and Ruler). This book will help you lea m to use. Additional titles in the series focus on other interactive geometry packages. This book contains a variety of geometric activities, each of which provides a context for exploration using interactive geometry software. The opening section approaches the introduction of the software through play, showing how to create a cartoon character based on line segments, and how to animate him. The second section relates the construction tools for creating points, lines and circles to the geometry of Euclid. Later sections provide an introduction to measurement, to transformation and to the exploration of loci in interactive geometry packages. Getting Started with Interactive Geometry Software 1

5 Geometry 1 PLAY Interactive geometry software offers an opportunity to explore geometry in new ways. There are many different software packages now available that offer this facility; all start from a similar set of basic tools. The image opposite shows an annotated version of the starting window for. The horizontal bar shows a section of menus. The lower horizontal bar shows the tool boxes. You can use: the Point tool box to plant points on a sketch sheet; the Line construction tool box for perpendicular, perpendicular lines, bisectors and tangents; the Compass tool box to construct circles; the Angle toolbox for set angles and distance; the Transformation toolbox to for reflection, rotation, enlargement and vector translation; the Straightedge tool box to construct line segments, rays or lines. To see inside the Straightedge tool box: Hold the mouse over the Straight edge tool. Press the left button and hold it down. This pulls out a menu of tools. Select tools from the menu by dragging the mouse to the tool you want and releasing the mouse button. You will first need to familiarise yourself with the tools in the software. The following activity will allow you to begin to do this by using the Segment tool from the Straight edge tool box. 2 Getting Started with Interactive Geometry Software

6 File Edit View Options Tools Window Help c== r=-"; =c;; Selection Point tool box Line construction tool box Geebra File Edit View Options Tools Window Help wi01arnl J 0aJ[f. ; :: : /K Line through two POints... _.... 1/ Segment oetween two points..",. Segment with given length from point /' Ray through two paints / Vector between two paints Vector from point t:,. Polygon [) Regular polygon Getting Started with Interactive Geometry Software 3