1. Getting Started with GeoGebra Geometry Workshop Ithaca College August 22, 2014 Teresa Moore & Dave Brown moore@ithaca.edu dabrown@ithaca.edu 1

2. 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. 2

3. Techniques & Tools in this Workshop 1.GeoGebra Website 2.Webstart vs. Applet Start 3.Basic GeoGebra Window 4. New Point tool 5. Move tool 6.Free and Dependent Objects 3 Getting Started with GeoGebra

4. Techniques & Tools in this Workshop 7.Commands  Save File  New vs. New Window 8.Grid and Axes – Turning on/off 9. Regular Polygon tool 10. Show Object / Show Label 4 Getting Started with GeoGebra

5. Techniques & Tools in this Workshop 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 5 Getting Started with GeoGebra

6. Techniques & Tools in this Workshop 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 6 Getting Started with GeoGebra

7. 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 7 Getting Started with GeoGebra

8. Techniques & Tools in this Workshop 25.Geometry Explorations and Tools menu 26.Lines vs. Linear Functions – not covered today 27. Spreadsheet View – not covered today  Cell Addresses  Inputting formulas with numbers/functions  Copying  Create List of Points 8 Getting Started with GeoGebra

9. Where is GeoGebra? 1.Open browser (Safari, FireFox, …) 2.Type in: geogebra.org 3.See Download link 9

10. First Time GeoGebra Download here Tabs CLICK NOW! 10

11. 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. 11

12. GeoGebra Tools Command Line GeoGebra Window 12

13. More GeoGebra Tools 13 GeoGebra Window

14. Algebra View Free Objects Dependent Objects GeoGebra Window 14

15. Graphics View DRAWING PAD 15 GeoGebra Window

16. Spreadsheet View GeoGebra Window 16

17. GeoGebra Window Input Bar Command List 17

18. 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) 18

19. 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. 19 Understanding Objects

20. Object Values Current Values 20

21. Object Definitions Definitions 21

22. 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. 22

23. Understanding Objects 23 anywhere along x-axis cannot move

24. 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 ways File -> New Window (Ctrl+N) opens new file without closing current file File -> New closes current file and opens new blank file 24

25. 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. 25

26. Dynamic Square Command: File -> New Turn on Grid – Right-click in blank space in Drawing Pad. – Select Grid 26

27. Dynamic Square Definitions of a square? – Regular polygon with 4 sides GeoGebra: Regular polygon tool 27

28. 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. 28

29. 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”. 29

30. 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! 30

31. 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! 31

32. Labels, Names and Values – We want to “label” the square with its area. 32

33. 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 33

34. Labels, Names and Values Step 2: Change the label from Name to Value. – Right-click inside of square. – Select Object Properties (bottom of list). 34

35. Labels, Names and Values – Object Properties: Basic Tab – Click on Close. 35

36. 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. 36

37. Object Properties Category: Segment 37

38. 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: 38

39. Save File – What’s next? 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. 39

40. 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). 40

41. 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. 41

42. Save File – What’s next? 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 42

43. 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. 43

44. 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. 44

45. 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! 45

46. 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. 46

47. 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. 47

48. More circles from the slider 1.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. 48

49. 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”. – Pan 1.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 49

50. 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 50

51. Fill in the circles with color – Drag Properties Window to side! Then you can see your changes! 51

52. Position Circles and Turn off Points 1.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. 52

53. Our result … 53

54. 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 54

55. 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. 55

56. 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. 56

57. 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 B 1 57

58. Dynamic Rectangle – Need vertex D. You know the tools: and. Try to do it yourself … 58

59. 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 tool Select Polygon tool and click on A, B, C, D and A. 59

60. Dynamic Rectangle 60

61. Dynamic Rectangle – Hide (don’t delete!) what you don’t want to see. – Color and decide on label displays. With everything Cleaned up 61

62. Hiding – not Deleting For fun, try deleting point B 1 – What happens? Why? Only free points A and C remain. The definition of line a depends on the point B 1. And everything else depends on line a. So without point B 1 …. Rule: When in doubt, hide it! – Undo deleting B 1 62

63. 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 Objects Then poly1 and click on OK. 63

64. Dynamic Rectangle Test that the text changes with the rectangle. – Activate the Move tool and change your rectangle. 64

65. Save File – What’s next? 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? 65

66. Exploration 1 Where should I live? Download the Explorations at faculty.ithaca.edu/dabrown/docs/Geometry_Aug2014 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 66

67. Exploration 1 Where 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? 67

68. Exploration 2 Using the Tools menu 1.Create a centroid tool a.Construct an arbitrary triangle b.Construct midpoint of each side c.Construct each median d.Use the Intersect Two Objects tool to create centroid e.Select the centroid (only the centroid) f.Choose Create New Tool... in Tools menu g.In the dialog box, the centroid should be listed as Output Objects h.Click Next (the triangle vertices appear as Input Objects) i.Name tool (such as Centroid), check the Show in Toolbar, and click Finish j.Now, tool appears in toolbar. k.Create another triangle and use the Centroid tool. 68

69. Exploration 2 Using 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? 69

70. Exploration 3 Nine Point Circle – from EngageNY Module 1 Go to Lesson 31 in Module 1 or Open Explorations 3 in download 70

71. Exploration 4 Where 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. 71

72. Exploration 4 Where 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? 72

73. Exploration 5 Four-bar linkage 73

74. Exploration 5 Four-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. 74

75. Exploration 5 Four-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? 75

76. Save File – What’s next? 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. 76

77. 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. 77

78. 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)! 78

79. 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) 79 1. Click in B1 to highlight it. 2. Click and drag little blue square (bottom right B1) down 1 cell to B2.

80. 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. 80

81. 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 81

82. Linear Function Save your file – Filename: whatever you like. 82

83. GeoGebraTube GeoGebraTube 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_Aug201 4 83