getting started with geogebra geometry workshop ithaca college august 22, 2014 teresa moore &...

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Getting Started with GeoGebra

Geometry WorkshopIthaca College

August 22, 2014

Teresa Moore & Dave [email protected]

[email protected]

mailto:[email protected]

mailto:[email protected]

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Standards for Mathematical Practice

• Make sense of problems and persevere in solving them.• Reason abstractly and quantitatively.• Construct viable arguments and critique the reasoning

of others.• Model with mathematics.• Use appropriate tools strategically.

• Attend to precision.• Look for and make use of structure.• Look for and express regularity in repeated reasoning.

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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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7. Commands Save File New vs. New Window

8. Grid and Axes – Turning on/off9. Regular Polygon tool10. Show Object / Show Label


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11. Object Properties - Changing Label Options – Right Pane: Basic Tab

Category – Left Pane: Selecting Multiple Objects

12. Undo and Redo

13. Polygon tool

14. Animation


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15. Slider tool

16. Circle with Center and Radius tool

17. Play and Pause buttons

18. Zoom and Pan (Move Drawing Pad)

19. Object Properties Fill – Right Pane: Style Tab

Color – Right Pane: Color Tab


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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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25. Geometry Explorations and Tools menu26. Lines vs. Linear Functions – not covered today27. Spreadsheet View – not covered today

Cell Addresses Inputting formulas with numbers/functions Copying Create List of Points


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Where is GeoGebra?1. Open browser (Safari, FireFox, …)

2. Type in: geogebra.org

3. See Download link

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First Time GeoGebra

Download here

Tabs

CLICK NOW!

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Getting started with GeoGebra

Can you install a program on your computer?– Yes Choose appropriate platform

Program will download and you install it once. You get icon on desktop and you start from there.

– No Use JAVA Applet Some school LANs do NOT allow you to install. So you will

use Applet Start each time within your browser.

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GeoGebra Tools

Command Line

GeoGebra Window

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More GeoGebra

Tools

GeoGebra Window

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Algebra View

Free ObjectsDependent Objects

GeoGebra Window

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Graphics View

DRAWING PAD

GeoGebra Window

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Spreadsheet View

GeoGebra Window

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GeoGebra Window

Input Bar

Command List

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Understanding Objects

• Objects - Algebraic– Free objects (dark blue)

you can click and drag them anywhere– Dependent objects

- Semi-dependent (light blue) you can click and drag them within their parent object

(i.e. the object on which they depend)

- Dependent (black) 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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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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anywhere

along

x-axiscannot move

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Save File – What’s next?

• Save your file– Standard command with filename: file_one– 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,d and 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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• Step 2: Change the label from Name to Value.– Right-click inside of square.– Select Object Properties (bottom of list).

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– 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.

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 your file– Filename: file_two (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 your file– Filename: file_three (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, oscillate or random.

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 key and 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 Point. Click on the Basic tab and deselect Show Label

Click on category Conic. Click on the Basic tab and deselect Show Label. Click on the Color tab and Click & drag Opacity to 50.– Click on each circle at left and then pick a color at right.

– You can also use drop down tools in the Graphics menu

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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: file_four(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. (Under New Point)• 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

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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 somewhere away from rectangle.

• Type Area =Choose ObjectsThen 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 your file– Filename: whatever you like

• New Goal: Geometry Explorations

– Using GeoGebra to explore

– Emphasis on Mathematical Practice Standards

– How would your students explain their work in these Explorations?

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Exploration 1Where should I live?• Download the Explorations at

faculty.ithaca.edu/dabrown/docs/Geometry_Aug2014• Open WhereToLive.ggb• The map was created in

Google Maps• I took a screen shot and

used the Insert Image tool

http://faculty.ithaca.edu/dabrown/docs/Geometry_Aug2014

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Exploration 1Where should I live?You are planning to move to Downtown Ithaca and you want be the same distance from from home to each of Wegmans, the Farmers' Market, and your Mom's house. Figure out the best location for your new home.

• Without doing anything else, make a reasonable guess as to where you should live.

• How would you go about solving this problem?• How did your solution compare with your initial guess?

Anything surprise you?

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Exploration 2Using the Tools menu

1. Create a centroid toola. Construct an arbitrary triangleb. Construct midpoint of each sidec. Construct each mediand. Use the Intersect Two Objects tool to create centroide. Select the centroid (only the centroid)f. Choose Create New Tool... in Tools menug. In the dialog box, the centroid should be listed as Output Objectsh. Click Next (the triangle vertices appear as Input Objects)i. Name tool (such as Centroid), check the Show in Toolbar, and click

Finishj. Now, tool appears in toolbar.k. Create another triangle and use the Centroid tool.

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Exploration 2Using the Tools menu

2. Use the centroid tool to discover a significant difference between the centroid of a triangle and the circumcenter created in Exploration 1.

3. Create an Orthocenter Tool (recall, the orthocenter is the intersection of altitudes of a triangle)

4. Explore the differences between the centroid, circumcenter, and orthocenter. Do they ever coincide?

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Exploration 3Nine Point Circle – from EngageNY Module 1• Go to Lesson 31 in Module 1 or • Open Explorations 3

in download

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Exploration 4Where Should the Mirror Go?This young lady wants to install a mirror so that she can see her whole body in the mirror without wasting material.

Use the accompanying GGB file to see the modeling power of GeoGebra and to explore questions on the next page.

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Exploration 4Where Should the Mirror Go?This young lady wants to install a mirror so that she can see her whole body in the mirror without wasting material.• What is the minimum possible length

of the mirror?• How high up the wall should the mirror

be mounted?• How from the mirror should she stand?

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Exploration 5Four-bar linkage

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Exploration 5Four-bar linkage• A four-bar linkage contains four links that

interconnect and rotate (or not).• The Frame link rigidly connects the linkage to another

system.• The Coupler is opposite the Frame and connects the

remaining two links.• The linkage may have 0, 1, or 2 links that completely rotate.

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Exploration 5Four-bar linkage• Download Linkage.ggb and explore• Use Construction Protocol (View Menu) to

see how I built it.• What conditions on the lengths of the links guarantees that

at least one link fully rotates? • Explore different lengths for the different links.• Make the Frame the longest side and make Link2 the

shortest. – How are the lengths of the Frame and Link2 related to other two

lengths when Link2 rotates completely?– What is the motion of Link1 in this case?

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• Save your geometry exploration files– Filenames: whatever you like

• 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. Linear Function• 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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Linear Function• 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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Linear Function• 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)

1. Click in B1 to highlight it.

2. Click and drag little blue square (bottom right B1) down 1 cell to B2.

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Linear Function• 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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Linear Function• 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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Linear Function

• Save your file– Filename: whatever you like.

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GeoGebraTubeGeoGebraTube is the official repository of GeoGebra constructions and GeoGebra related resources.• http://www.geogebratube.org/

Today’s GeoGebra Materials available at http://faculty.ithaca.edu/dabrown/docs/Geometry_Aug2014

http://www.geogebratube.org/





getting started with geogebra geometry workshop ithaca college august 22, 2014 teresa moore &...

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