Geogebra

Introduction: the GeoGebra window

The GeoGebra screen is divided in several sections to represent mathematical objects in different

ways. The names of the different parts are shown below.

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m43b4d032.gif Main Screen - GeoGebra

Menu Bar: It is a typical windows command menu bar. File, Edit, View etc... are called the menu-items.

Tool Bar: It has all the tools (compass box) to use in the graphic view.

Active Tool View: It tells you which tool is active to use on the graphic view and how to use it.

Graphic View: It is used to draw the geometric figures (also called objects in GeoGebra). This window can never be closed.

Algebra View: It shows the algebraic expressions. This window can be closed if you are working only on geometry.

Input Bar: This is used to enter more complex mathematical expressions that may not be available on the Tool Bar.

Commands: It has to be used along with the Input Bar, to select from a list of available commands.

The Toolbar

The tool bar is GeoGebra's compass box

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 48e11462.png Each tool has many related tools under it. To see all the related tools, click on the arrow at the bottom right hand corner of each tool as shown below.

Basic use of tools

• File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m2e9355f9.pngActivate a tool by clicking on the button showing the corresponding icon.
• Open a toolbox by clicking on the lower part of a button and select another tool from this toolbox.

Look of screen

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 156af86e.pngIn GeoGebra only the graphic view cannot be closed. You can change the screen to be best fit for working with your needs: Press View on the menu Item and uncheck or check Algebra View, Axes and Grid based on your needs.

GeoGebra Exercises

1. Drawing points, line segment and rays

To learn how to use GeoGebra we will use the most commonly used tools when drawing geometrical shapes .

1. Select Point Tool, and click anywhere on the drawing point to plot six points A, B, C, D, E, F.
2. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 6802121.pngSelect Segment between two points tool, click on point A and then point B.
3. Select Line through two points tool, click on point C and then point D.
4. Select Ray through two points tool, click on point E and the point F.

Can you describe in your own words the difference between a segment, line and ray? Also see the algebra view and observe the equations of the line b and ray c. The line segment a is represented in the algebra view as a = 2.83, where 2.83 is the length of the segment.

1. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 1eb2590.pngDrawing a parallel line
   1. Select Point Tool and click anywhere on the drawing point to plot three points A,B, C.
   2. Select Line through two points tool, click on point A and then point B.
   3. Select Parallel Line tool, click on point C first. Then click on line AB.

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m779a848b.gifNow use the Move Tool move points A, B and C. What do you observe? Describe it.

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 3c7f10aa.gifNext use the Move Graphics view tool and move the drawing pad. Do the two lines ever meet?

1. Drawing polygons
   1. Select Point tool and plot three points A B and C to represent the vertices of a triangle.
   2. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m54b722a1.pngTo draw a three-sided polygon – triangle, select Polygon tool click on point A, then B and C and again click on point A. OR

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html mab953ed.pngTry making a pentagon and hexagon on your own.

1. Rotate a ray
   1. Draw line segment AB of any length' (Segment between two points tool)'.
   2. Select the Ray Through two points tool, click on point A, then select another point C on the drawing pad as shown in the figure.
   3. Select the Angle tool, as seen in the figure and click on points B, then A and finally C. You will see an angle measure. Click on the Move tool and move point C. Observe the change of angle.
   4. Observe the direction (clockwise, anticlockwise) in which you move the ray? In which direction does the angle increase and which direction does it decrease?
3. Draw triangles

In this exercise you are going to draw a right-angled triangle where the base is 5 units and the hypotenuse is 8 units.

All buttons on the tool bar hide many related tools. You choose the tool you want by pressing the small red arrow in the lower right corner of the button. Choose from the list that shows up.

1. Start your drawing by using the tool Segment with Given Length from Point.

1. Continue by drawing the right angle. Do this by drawing a perpendicular line through point A. Choose the perpendicular line tool, click on point A first and then on the line.

1. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 72a9f629.pngTo mark the third corner of the triangle you use one of the circle tools, Circle with Centre and Radius.
2. Click on the point B and fill in the length of the hypotenuse as radius.

1. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m5680d7e4.pngChoose the tool Intersect Two Objects, click on the circle and the perpendicular line. The point in the intersection is the third corner of the triangle.

1. Draw the triangle by choosing the Polygon tool. You need to click all the corners and then click again on the first corner to complete the triangle.

1. The perpendicular line and the circle, even the points do not need to be visible or seen now, you only want to show the triangle. Hide an object by right-clicking the object and uncheck Show Object by clicking on it.

1. To save your GeoGebra file, select menu item File > Save As.
2. Select the Document folder.
3. Type the filename Right Angled Triangle.
4. The Files of Type box will automatically have Geogebra Files (.ggb).
5. Click Save. Your file will be saved as Right Angled Triangle.ggb.

File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html 643eb27c.pngTo open GeoGebra files

1. Open the GeoGebra applications.
2. Select menu item File > Open.
3. Select the folder and the file.
4. Click Open.

Additionally you can try the following exercise.

1. Follow the following steps to construct a rectangle ABCD like the figure. Use the Move tool and move the vertices of the rectangle. If you have constructed the rectangle correctly, when you move the vertices the figure will always be a rectangle. Seeing this construction can you write down the properties of a rectangle? Steps:
   1. Draw a line segment AB of any length (Segment between two points tool).
   2. Draw a perpendicular line at point A perpendicular to line segment AB. For this in GeoGebra : Select the Perpendicular line tool. Click on point A then select line segment AB. File:ICT Phase 3 - Resource Book 8th Standard ENGLISH - 70 Pages html m7091d368.png
   3. Similarly draw another perpendicular line at point B to line segment AB. How will you do this in GeoGebra?
   4. Now select the 'Parallel Line tool and draw a parallel line to AB at any new point C'.
   5. Mark the intersection points of the parallel and perpendicular lines as D and E using the Intersect two objects tool.
   6. ADEB the rectangle you constructed.
   7. To measure the sides, use the Distance or Length tool and click on points AD, then DE, then EB and finally AB.
   8. Select the move tool and move points A or B. What do you observe, write down your observations.
   9. Now use the polygon tool and complete your rectangle. Also hide the construction. How will you do this?