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Workshop 1
GeoGebra-NA2010 1
Techniques & Tools in this Workshop
1. GeoGebra Website2. Webstart vs. Applet Start3. Basic GeoGebra Window4. New Point tool5. Move tool6. Free and Dependent Objects
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Getting Started with GeoGebraTechniques & Tools in this Workshop
7. CommandsSave FileNew vs. New Window
8. Grid and Axes – Turning on/off9. Regular Polygon tool10. Show Object / Show Label
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Getting Started with GeoGebra
Techniques & Tools in this Workshop
11. Object Properties - ChangingLabel Options – Right Pane: Basic Tab
Category – Left Pane: Selecting Multiple Objects
12. Undo and Redo
13. Polygon tool
14. Animation
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Getting Started with GeoGebraTechniques & Tools in this Workshop
15. Slider tool16. Circle with Center and Radius tool17. Play and Pause buttons18. Zoom and Pan (Move Drawing Pad)19. Object Properties
Fill – Right Pane: Style TabColor – Right Pane: Color Tab
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Getting Started with GeoGebra
Techniques & Tools in this Workshop
20. Line through 2 Points tool
21. Perpendicular line tool
22. Parallel line tool
23. Intersect 2 Objects tool
24. Insert Text tool
Dynamic Text
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Getting Started with GeoGebra
Techniques & Tools in this Workshop
25. Lines vs. Linear Functions26. Spreadsheet View
Cell AddressesInputting formulas with numbers/functionsCopyingCreate List of Points
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Getting Started with GeoGebra
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Getting Started with GeoGebraWhere is GeoGebra?
1. Open browser (Internet Explorer, FireFox, …)2. Type in: geogebra.org3. See button for Download
4. See tabs for
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First Time GeoGebra
Download Button
Tabs
CLICK NOW!
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GeoGebra Download Page
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http://www.geogebra.org/cms/en/download
Getting started with GeoGebra
Can you install a program on your computer?– Yes Use WebStart or Offline Installer
Program will download and you install it once. You get icon on desktop and you start from there.
Webstart checks for updates each time it runs.Offline installs once.
– No Use Applet StartSome school LANs do NOT allow you to install. So you will use Applet Start each time within your browser.
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RIGHT NOW
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During the break – you can install GeoGebra on your laptop.
GeoGebra Download Pagehttp://www.geogebra.org/cms/en/download
GeoGebra Tools
Command Line
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GeoGebra WindowTitle Bar
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GeoGebra Window
More GeoGebra
Tools
Algebra View
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Free ObjectsDependent Objects
GeoGebra Window
Graphics View
DRAWING PAD
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GeoGebra Window
Spreadsheet View
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GeoGebra Window
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GeoGebra Window
Input Bar
Command List
Special Characters
Understanding Objects• Objects - Algebraic
– Free objects (dark blue color)you can click and drag them anywhere
– Dependent objects- Semi-dependent (light blue color)
you can click and drag them within their parent object (i.e. the object on which they depend)
- Dependent (black color)you cannot drag them* (they will move with their parent object)
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• Activate (click on) the New point tool
• Click once inside the first quadrant.– You will get a free point A.
• Click again somewhere along the x-axis.– You will get a semi-dependent point B.
• Click again on (0,0).– You will get a (completely) dependent point C.
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Understanding Objects Object Values
Current Values
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Object Definitions
Definitions
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Moving Objects• Activate (click on) the Move tool• Click and drag point A.
It will go anywhere.
• Click and drag point B.It will only go along the x-axis.
• Click and drag C.It won’t move.
Important: GeoGebra is case-sensitive! A is NOT a.
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Understanding Objects• Objects - Algebraic
– Free objects (dark blue color)you can click and drag them anywhere
- Semi-dependent (light blue color)you can click and drag them within their parent object
(within the object on which they depend)
- Dependent (black color)you cannot drag them
(they will move with their parent object)
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Understanding Objects
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anywhere
along x-axisalong x-axis
cannot move
cannot move
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Save File – What’s next?
• Save your file– Standard command with filename: lfs_ws1-1– File type is ggb
• New Goal: Create a Dynamic Square
• New File – 2 waysFile -> New Window (Ctrl+N)
opens new file without closing current fileFile -> New
closes current file and opens new blank file
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New Window vs. New
New Window: Opens another “instance” of GeoGebra. Now you have 2 files open.
New: Closes current file. Opens new (blank) file.
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Dynamic Square• Command: File -> New• Turn on Grid
– Right-click in blank space in Drawing Pad.– Select Grid
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Dynamic Square• Definitions of a square?
– Regular polygon with 4 sides• GeoGebra: Regular polygon tool
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Dynamic Square– Regular polygon with 4 sides
• Select and click once to get Point A.
• Click again to get Point B.
• Dialog box will open … 4 is there… click on OK.
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Dynamic Square– Regular polygon with 4 sides
Notice: The values of a, b, c and d are their lengths.The value of poly1 is its area.
Points A and B are FREE objects.
Segments a,b,c,dand poly1 are
“together”.
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Square Dynamics• What can you move?
– Before moving, you need to select Move tool.
– You can click and drag point A or point B.• Since these are free points, you can change the
dimensions of the square – but notice that it is always a square!
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Square Dynamics– You can click and drag point A or point B.
– You can click and drag the square itself.This will only move the square
- the dimensions of the square depend on A and B!
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Labels, Names and Values– We want to “label” the square with its area.
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Labels, Names and Values• Step 1: Turn on the label.
– Right-click inside of square. – Click on Show Label.
– By default, the label is the Name of the object.• Here the name is poly1
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Labels, Names and Values• Step 2: Change the label from Name to Value.
– Right-click inside of square.– Select Object Properties (bottom of list).
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Labels, Names and Values– Object Properties: Basic Tab
– Click on Close.
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Object Properties• Let’s do that again.
– Right-click on ANY object; select Object Properties.or Edit -> Properties or Ctrl+E
In the Object Properties windows …– Choose an object or category in the left pane.
• Move this window off to the right so you see changes as you make them.
• Try the options on other tabs!
• Click on Close when you are done.
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Object Properties
Category:Segment
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Undo and Redo• Forget to change to the Move tool?
– Oops, I created objects I don’t want.• Don’t like your changes?
– Undo
– Redo Here:
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Save File – What’s next?
• Save your file– Filename: lfs_ws1-2 (or whatever).
• New Goal: When is a square not a square?Use Polygon tool to create a “square”.
Use Move tool to move any of the vertices
and change the shape of this quadrilateral.
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Square – not a Square?• Command: File -> New
– Polygon tool• Click at (-1,-1), (4,-1)
(4,4), (-1,4)(or any 4 square points)
• Click again on A.(Make it say Point A!)
– You see a square. – But all 4 vertices are blue = free.– You have a quadrilateral (4-sided polygon).
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Square – not a Square?– You have a quadrilateral (4-sided polygon).
Now – not to be boring … too late .Please notice that we NEVER clicked on the axes!
because we don’t want our points “tied” to the axes.
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Save File – What’s next?
• Save your file– Filename: lfs_ws1-3 (or whatever).
• New Goal: Create an Animation– Use Slider tool to define radius
– Use Circle with center and radius tool
… to make circles with various radii.
– Animate the circles
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Animation – Slider first• Command: File -> New
• Turn off Grid (right-click in DP, click on Grid).
• Turn off Axes (right-click in DP, click on Axes).
• We create a slider – why?– Sliders can be animated -
either manually (click & drag) or automatically (play & pause)
– Slider is a number whose value can be changed.
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Animation - Slider first• Make a slider a from [0,2] increment 0.01 .
– Select Slider tool .– Click in the Drawing pad (upper right).– Type 0 (min), 2 (max) and 0.01 (increment)
– Click on Apply.
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Circles from the slider– Want circles whose radii depend on the slider.
• Select Circle with center and radius tool.
• Click in the Drawing pad (to get center point A).
• Type a in the dialog box and click on OK.
• The radius of the circle is the value of the slider!
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Automated Animation• Turn on animation
– Right-click on slider.– Click on Animation on.
Slider will start to move.
Radius of circle will increase and then decrease.
Pause/ Play button is in bottom left of Drawing Pad.
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Manual Animation• Press the Pause button• Activate the Move tool.• Click and drag the slider point to change the value
of a manually.
Sliders can be set to increase, decrease or oscillate.
Both manual and automated animation work “better” if the width of the slider is a multiple of interval of the slider.
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More circles from the slider1. Again, select Circle with center and radius tool.2. Click in the Drawing pad (to get center point B).3. Type a/2 in the dialog box and click on OK.
• Repeat 1-3 with radius a/3• Repeat 1-3 with radius 2*a• Repeat 1-3 with radius 3*a
– Press Play button to animate again.
– Use Move tool to click and drag circles.
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Zooming and Panning– Zoom
1. Use your mouse scroll button to zoom in and out.– Place mouse pointer in Drawing pad and scroll.
2. Use Zoom out tool and Zoom in tool.
3. Zooming is not “undoable”.
– Pan1. Use shift + mouse click & drag to pan
– Place mouse pointer in Drawing pad, press and hold Shift keyand then click & drag mouse.
2. Use Move drawing pad tool.
3. Panning can be “undone”. Use
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Fill in the circles with color– Fill the circles
1. Right-click on any circle and choose Object properties.2. Click and drag the Properties window to one side so you
can see the Drawing pad. Click on category Points.
Click on the Basic tab and deselect Show Label* Click on category Circle.
Click on the Basic tab and deselect Show Label.Click on the Style tab and Click & drag Filling to 50.Click on the Color tab.
– Click on each circle at left and then pick a color at right.
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Fill in the circles with color– Drag Properties Window to side!
Then you can see your changes!
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Position Circles and Turn off Points1. Position your circles before you turn off the points!
2. Right-click on any object and choose Object properties.
3. Click on the category Points and on the Basic tab and deselect Show object.
• If you want to re-position the circles, you must first turn-on the points again.
• To do this, right-click on any object and select Object properties. (Ctrl+E)
• Now you have access to the Points again! Turn them on and then re-position.
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Our result …
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Save File – What’s next?• Save your file
– Filename: lfs_ws1-4 (or whatever).
• New Goal: Create a Rectangle – We want A and C to be the free vertices.
– Use Line tool to create base line.
– Use tools perpendicular (and parallel )
– Use tool Intersect 2 objects
– Dynamic Text with tool
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Dynamic Rectangle• Command: File -> New• Make a base line
– Select the Line tool .– Click left Point A, then right Point B and we get line a.
Point A is bottom left vertex of rectangle.Point B is just a point!
• Make Point C top right vertex of rectangle.– Select New point tool and
– Click once in top right to get Point C.
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Dynamic Rectangle– Need a perpendicular at Point C to line a.
• Select Perpendicular line tool.
• Click once on Point C (make it glow).
• Click once on line segment a (make it glow).– You get a line b perpendicular to the base line a through C.
– Need intersection point of line a and line b. • Select Intersect two objects tool.• Click on the intersection point of the two lines.
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Dynamic Rectangle– Rename this point B.
• Right-click on point D.
• Select Rename from list.
• Type in B and click on OK.
• Notice “old” B is renamed B1
– Need intersection point of line a and line b. • Select Intersect two objects tool.• Click on the intersection point of the two lines.
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Dynamic Rectangle
– Need vertex D.You know the tools: and .Try to do it yourself …
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Dynamic Rectangle– Need vertex D.
Select Perpendicular line tool• Click on Point C and then on line b.• Click on Point A and then on line a.
Select Intersection of two objects tool• Click on intersection point of the new lines.
– Make the rectangle using the polygon toolSelect Polygon tool and click on A, B, C, D and A.
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Dynamic Rectangle
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Dynamic Rectangle– Hide (don’t delete!) what you don’t want to see.– Color and decide on label displays.
With everything Cleaned up
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Hiding – not Deleting• For fun, try deleting point B1
– What happens? Why?• Only free points A and C remain.• The definition of line a depends on the point B1.• And everything else depends on line a.• So without point B1 ….
Rule: When in doubt, hide it!
– Undo deleting B1
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Dynamic Text– Want text that tells the Area of the rectangle
Select Insert text tool• Click in Drawing pad underneath sliders.
• Type (including double quotes!)"Area = "+poly1 and click on OK.
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Dynamic Rectangle• Test that the text changes with the rectangle.
– Activate the Move tool and change your rectangle.
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Save File – What’s next?
• Save your file– Filename: lfs_ws1-5.
• New Goal: Create a Function & Spreadsheet
– Use Input bar to create a function
– Use function to create a spreadsheet.
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Line vs. Function of Line• Command: File -> New
• Click in the Input Bar (bottom left)– Type y=-x+4 and hit Enter.
• This is a line
– Type f(x)=-x+4 and hit Enter.• This is the same line, but now it is a function.
• We have done many things with lines.
• We can do different things with functions.
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Function of Line• Want a table of values for this function
• We will make a table for 6 x-values
x = 0,1,2,3,4,5
• Open the Spreadsheet– Command: View -> Spreadsheet
VERY IMPORTANT: Spreadsheet cells are ALWAYS a capital letter (case-sensitive)!
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Function of Line• Click in A1 and type 0 and hit Enter.
• Click in B1 and type =f(A1) and hit Enter.
• Click in A2 and type =A1+1 and hit Enter.
• READY TO COPY B1 to B2 (just like Excel)
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1. Click in B1 to highlight it.
2. Click and drag little blue square (bottom right B1) down 1 cell to B2.
Function of Line• READY TO COPY A2 and B2 down
– Click in A2 and drag to B2 to highlight both cells.
– Click and drag little blue corner of B2 down to B6.
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Function of Line• Make a list of the points.
– Click in A1 and drag to B6 to highlight A1:B6.
– Right-click on one of marked cells.
– Select: Create List of Points
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Function of Line
• Save your file– Filename: lfs_ws1-6 (or whatever).
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