GeoGebra 3D: Beginner Tutorials with Lesson Ideas
1. Beginner Exercises
1. GeoGebra 3D Beginner Tutorial: Exercise 1
2. GeoGebra 3D Beginner Tutorial: Exercise 2
2. Intermediate Exercises
1. 4 Ways to Quickly and Easily Construct an Equilateral Triangle With Vertices on Both xAxis and zAxis
2. 4 Ways to Build a Cylinder (H = 2R)
3. 4 Ways to Build a Cone

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GeoGebra 3D: Beginner Tutorials with Lesson Ideas

Tim Brzezinski, Jun 27, 2019

This GeoGebra book (currently under construction) contains exercises to help new users take a baby-step approach with becoming familiar with GeoGebra's 3D Calculator app. EACH EXERCISE CONTAINS ONLY THE TOOLS YOU NEED to complete a particular construction. [b]Teachers: [/b] By engaging with each exercise, you will experience JUST HOW EASY it is to use GeoGebra 3D Calculator. More importantly, you'll also actively experience how it can serve as a POWERFUL platform for student-centered discovery of several concepts students learn within the mathematics curriculum. 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

Beginner Exercises
1. GeoGebra 3D Beginner Tutorial: Exercise 1
2. GeoGebra 3D Beginner Tutorial: Exercise 2
Intermediate Exercises
1. 4 Ways to Quickly and Easily Construct an Equilateral Triangle With Vertices on Both xAxis and zAxis
2. 4 Ways to Build a Cylinder (H = 2R)
3. 4 Ways to Build a Cone

1.

Beginner Exercises

1. GeoGebra 3D Beginner Tutorial: Exercise 1
2. GeoGebra 3D Beginner Tutorial: Exercise 2

1.1.

GeoGebra 3D Beginner Tutorial: Exercise 1

NEW TOOLS WE WILL LEARN HOW TO USE:

Move [icon]/images/ggb/toolbar/mode_move.png[/icon][br]Point [icon]/images/ggb/toolbar/mode_point.png[/icon][br]Plane Through 3 Points [icon]/images/ggb/toolbar/mode_planethreepoint.png[/icon][br]Intersect Two Surfaces [icon]/images/ggb/toolbar/mode_intersectioncurve.png[/icon][br][br][b][color=#1e84cc]In this introductory exercise, we'll learn a means through which students can discover the intersection of any 2 (non-parallel) planes. [/color][/b]

DIRECTIONS:

1) Select the POINT [icon]/images/ggb/toolbar/mode_point.png[/icon] tool. Use this tool to plot 3 points anywhere on the gray plane. [br][br]2) Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] arrow. Click twice on any one of the points you plotted in step (1).Use this tool to [br] move this point off of the gray plane. Repeat this process for the other 2 points. [br][br]3) Select the PLANE THROUGH 3 POINTS [icon]/images/ggb/toolbar/mode_planethreepoint.png[/icon] tool. With this tool highlighted, select the 3 points you [br] initially plotted in step (1). This will create a plane that passes through these 3 points. [br] [b] [br] Note:[/b] This step could have also been done without plotting the points first (step 1).[br] Steps (1) - (2) were included here simply to acquaint you with plotting & moving points in 3D. [br][br][b][i]Further directions appear below this applet. [/i][/b]

4) Select the MOVE [icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon] arrow. Use this tool to drag any one (or more) of these 3 points around. Notice [br] how the plane you plotted in (3) always passes through these 3 points. [br][br]5) Now select the INTERSECT 2 SURFACES [icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersectioncurve.png[/icon] tool. Select the plane you plotted in step (3). Then select [br] the gray plane. This will now plot the intersection of these 2 surfaces (here, planes).

QUESTION:

What can we conclude about the intersection of any 2 non-parallel planes?

[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

1.2.

2.

Intermediate Exercises

1. 4 Ways to Quickly and Easily Construct an Equilateral Triangle With Vertices on Both xAxis and zAxis
2. 4 Ways to Build a Cylinder (H = 2R)
3. 4 Ways to Build a Cone

2.1.

4 Ways to Quickly and Easily Construct an Equilateral Triangle With Vertices on Both xAxis and zAxis

Final Product:

Method 1: Simply plot 2 points on the xAxis. Then use Pythagorean Theorem to determine coordinates of 3rd vertex on zAxis.

Method 2: Use the REGULAR POLYGON tool to build directly on gray coordinate plane. Then rotate everything 90 degrees about the xAxis.

Method 3: Compass and straightedge constructions in MIDAIR? Absolutely! Here, we simply use the CIRCLE WITH CENTER THROUGH POINT tool twice. Note how we need to specify an axis of the circle as well (since we are in 3D).

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