GeoGebra Geometry

Tim Brzezinski, Natalie Burrows, Jul 21, 2019

[color=#1551b5]This GeoGebra book contains 21 exercises to help new users become familiar with GeoGebra's Geometry app[/color]. [b]EACH EXERCISE CONTAINS ONLY THE TOOLS YOU NEED[/b] to complete a particular construction. [b][color=#0a971e]Teachers: [/color][/b] By engaging with each exercise, you will experience JUST HOW EASY it is to use GeoGebra. More importantly, you'll also actively experience how it can serve as a POWERFUL platform for student-centered discovery of several concepts students learn in a Geometry course. Each exercise also contains a silent screencast that illustrates how to complete each construction (in case you're unsure of something or ever get stuck). I wish you much success on your journey of teaching and/or learning mathematics! Best, Tim Brzezinski

Table of Contents

  1. Beginner Exercises (1)
    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. Isosceles Triangle Exp: Ex. 5B
    7. Constructing Angles: Ex. 6
    8. Parallels & Perpendiculars: Ex. 7
  2. Beginner Exercises (2)
    1. Working With Midpoints: Ex. 8
    2. Making Perpendicular Bisectors: Ex. 9
    3. Vertical Angles Discovery: Ex. 10
    4. Constructing Angle Bisectors: Ex. 11
    5. Constructing Tangents: Ex. 12
    6. Sliders & Circles Discovery: Ex. 13
    7. Controlling Angles with Sliders: Ex. 14
    8. Exploring Slopes of Lines: Ex. 15
  3. Beginner Exercises (3)
    1. Translating by Vector: Ex. 16
    2. Rotating Around Points: Ex. 17
    3. Reflecting About Lines: Ex. 18
    4. Exploring Dilations: Ex. 19
    5. Composing Transformations: Ex. 20

1.

Beginner Exercises (1)

  • 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. Isosceles Triangle Exp: Ex. 5B
  • 7. Constructing Angles: Ex. 6
  • 8. Parallels & Perpendiculars: Ex. 7

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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2.

Beginner Exercises (2)

  • 1. Working With Midpoints: Ex. 8
  • 2. Making Perpendicular Bisectors: Ex. 9
  • 3. Vertical Angles Discovery: Ex. 10
  • 4. Constructing Angle Bisectors: Ex. 11
  • 5. Constructing Tangents: Ex. 12
  • 6. Sliders & Circles Discovery: Ex. 13
  • 7. Controlling Angles with Sliders: Ex. 14
  • 8. Exploring Slopes of Lines: Ex. 15

2.1.

Working With Midpoints: Ex. 8

DIRECTIONS:
1) Use the MIDPOINT [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] tool to plot the midpoints of any 2 sides of the given triangle. [br]2) Use the SEGMENT [icon]/images/ggb/toolbar/mode_segment.png[/icon] tool to draw the segment (triangle midsegment) connecting these 2 points.[br]3) Use ANOTHER TOOL to illustrate this midsegment (MS) is parallel to the 3rd side of the triangle. [br][br]4) Measure and display the names lengths of the MS and the side of the triangle the MS doesn't touch.[br][br]5) In the algebra view (left side), input [name of MS] / [name of triangle side MS doesn't touch]. [br][br]6) Move [i]A, B[/i], and/or [i]C[/i] around to verify the slopes are equal and the ratio MS / 3rd side = 0.5.
7)
Can you use YET ANOTHER TOOL to prove the midsegment is parallel to the 3rd side of the triangle? [br]Do so.
[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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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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3.

Beginner Exercises (3)

  • 1. Translating by Vector: Ex. 16
  • 2. Rotating Around Points: Ex. 17
  • 3. Reflecting About Lines: Ex. 18
  • 4. Exploring Dilations: Ex. 19
  • 5. Composing Transformations: Ex. 20

3.1.

Translating by Vector: Ex. 16

DIRECTIONS:
In the applet below,[br][br]1) Construct a triangle. [br]2) Use the VECTOR TOOL [icon]/images/ggb/toolbar/mode_vector.png[/icon] to construct any vector whose terminal points DOES NOT lie on top of its initial point. [br][br]3) Display the label of [b]the triangle's 3 vertices[/b] and [b]vector [/b]you've just constructed. [br] Use the "Name and Value" option when showing the label. [br] [br]4) Use the TRANSLATE BY VECTOR TOOL [icon]/images/ggb/toolbar/mode_translatebyvector.png[/icon] to translate the triangle by the given vector.
5)
Suppose the coordinates of a point [i]P = [/i]([i]x[/i], [i]y[/i]). What is the image of [i]P[/i] under a translation by vector with components <[i]a[/i], [i]b[/i]>?
[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

3.2.

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3.3.

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3.4.

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3.5.

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