GeoGebra: Beginner Exercises

Tim Brzezinski, SAVAŞ ORHAN, Apr 28, 2018

Contains exercises (with silent screencast tutorials following each exercise) to help new users get more familiar with GeoGebra. Each exercise (i.e. construction) contains ONLY THE TOOLS NEEDED to complete such a construction.

Table of Contents

  1. Beginner Exercises (L1)
    1. Creating Regular Polygons: Ex. 1
    2. Using Circle and Intersect Tools: Ex. 2
    3. Using the Compass Tool: Ex. 3
    4. Measuring Angles: Ex. 4
    5. Isosceles Triangle Exp: Ex. 5A
    6. Constructing Angles: Ex. 6
    7. Parallels & Perpendiculars: Ex. 7
    8. Working With Midpoints: Ex. 8
    9. Making Perpendicular Bisectors: Ex. 9
    10. Vertical Angles Discovery: Ex. 10
  2. Beginner Exercises (L2)
    1. Constructing Angle Bisectors: Ex. 11
    2. Constructing Tangents: Ex. 12

1.

Beginner Exercises (L1)

  • 1. Creating Regular Polygons: Ex. 1
  • 2. Using Circle and Intersect Tools: Ex. 2
  • 3. Using the Compass Tool: Ex. 3
  • 4. Measuring Angles: Ex. 4
  • 5. Isosceles Triangle Exp: Ex. 5A
  • 6. Constructing Angles: Ex. 6
  • 7. Parallels & Perpendiculars: Ex. 7
  • 8. Working With Midpoints: Ex. 8
  • 9. Making Perpendicular Bisectors: Ex. 9
  • 10. Vertical Angles Discovery: Ex. 10

1.1.

Creating Regular Polygons: Ex. 1

DIRECTIONS:
In the GeoGebra applet below,[br][br]1) Select the REGULAR POLYGON [icon]/images/ggb/toolbar/mode_regularpolygon.png[/icon] tool. Then plot 2 points [i]A[/i] and [i]B[/i]. [br] In the pop-up box that appears, enter "3" (without the " "). [br] This creates an "regular triangle" (equilateral & equiangular triangle). [br][br]2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon. [br][br]3) Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the [b][color=#1e84cc]blue points[/color][/b] around. [br] Note these polygons always remain regular. [br][color=#0000ff][br]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.[/color]
Quick (Silent) Demo
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

Beginner Exercises (L2)

  • 1. Constructing Angle Bisectors: Ex. 11
  • 2. Constructing Tangents: Ex. 12

2.1.

Constructing Angle Bisectors: Ex. 11

DIRECTIONS:
1) Use the ANGLE BISECTOR [icon]/images/ggb/toolbar/mode_angularbisector.png[/icon] tool to construct the 3 angle bisectors of the triangle. [br][br]2) Use the INTERSECT [icon]/images/ggb/toolbar/mode_intersect.png[/icon]tool to plot the point of concurrency (incenter) of these 3 angle bisectors. [br][br]3) Go to the algebra view (left side). [br] Hide the 3 angle bisectors of this triangle (you've just constructed in step 1). [br][br]4) Use the PERPENDICULAR LINE [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] tool to construct a line that passes through the incenter and is perpendicular to [math]\overline{DE}[/math]. [br][br][color=#0000ff]Further directions appear below the applet. [/color]
5) Use the PERPENDICULAR LINE tool to construct a line that passes through the incenter and is perpendicular to [math]\overline{EF}[/math]. [br][br]6) Use the PERPENDICULAR LINE tool to construct a line that passes through the incenter and is perpendicular to [math]\overline{DF}[/math]. [br] [br]7) Use the INTERSECT tool to plot the 3 points at which the lines (you constructed in steps 4 - 6) intersect the 3 sides of the triangle. [br][br]8) Go to the STEPS window. Hide the 3 lines you constructed in steps 4 - 6. [br][br]9) Construct a circle with centered at the incenter that passes through any 1 of the points you constructed in step 7.
10)
What do you notice? Why does this occur?
[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet. [/color]
Quick (Silent) Demo
– Tim Brzezinski

2.2.

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