Background Information

What is GeoGebra?
[size=100][left]GeoGebra is Dynamic Mathematics Software for all levels of education that brings together geometry, algebra, functions, spreadsheets, graphing, statistics, and calculus in one easy-to-use package. [br][br]GeoGebra is a rapidly expanding community of millions of users located in just about every country. [br][br]GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide.[/left][/size]
GeoGebra Web App user interface
Quick facts
[list][*][size=100]Geometry, Algebra and Spreadsheet are connected and fully dynamic[br][/size][/*][*][size=100]Computer Algebra System for symbolic calculations[/size][/*][*][size=100]3D Graphics View available[/size][/*][*][size=100]Easy-to-use interface, yet many powerful features[br][/size][/*][*][size=100]Authoring tool to create interactive learning materials as web pages[br][/size][/*][*][size=100]Available in many languages for our millions of users around the world[br][/size][/*][*][size=100]Open source software [url=https://www.geogebra.org/license]freely available for non-commercial users[/url][/size][/*][/list][size=100][br][/size]
GeoGebra webpage
[size=100]For more information about GeoGebra please check out our webpage [url=https://www.geogebra.org]www.geogebra.org[/url].[br][/size]

How to Use GeoGebra's Tools

What are Tools?
Each GeoGebra [i]View [/i]provides a [i]Toolbar [/i]with a selection of [i]Tools [/i]specific for the [i]View [/i]you are working with. You may activate a [i]Tool [/i]by clicking on the button showing the corresponding icon.[br][br][b]Task[/b]: Explore the [icon]/images/ggb/toolbar/mode_circle2.png[/icon] [i]Circle with Center through Point[/i] tool[br][list=1][*]Select the tool [img]https://wiki.geogebra.org/uploads/thumb/f/fb/Mode_circle2.svg/16px-Mode_circle2.svg.png[/img] [i]Circle with Center through Point[/i] from the [i]Graphics View Toolbar[/i].[/*][*]Click in the [i]Graphics View[/i] twice in order to create a circle.[br][u]Note[/u]: The first click defines the center of the circle, while the second click determines its size.[/*][*]Select the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move [/i]tool and drag the points in order to change the circle's size and / or position.[/*][/list]
Try it yourself...
What are Toolboxes?
GeoGebra's [i]Tools[/i] are organized in [i]Toolboxes[/i], containing similar [i]Tools [/i]or [i]Tools [/i]that generate the same type of new object. You can open a [i]Toolbox [/i]by clicking on the lower part of a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][br][b]Task[/b]: Find the [icon]/images/ggb/toolbar/mode_segment.png[/icon] [i]Segment[/i] tool within the [i]Toolboxes[/i][br][list=1][*]Search the [i]Toolboxes [/i]for the [img]https://wiki.geogebra.org/uploads/thumb/0/0c/Mode_segment.svg/16px-Mode_segment.svg.png[/img] [i]Segment [/i]tool[br][/*][*]Click in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img]  [i]Graphics View[/i] twice in order to create two points and a segment between them.[/*][*]Select the [img]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/16px-Mode_move.svg.png[/img] [i]Move [/i]tool and drag the points in order to change size and / or position of the segment.[br][/*][/list]
What are Tooltips?
If you select a [i]Tool[/i], a [i]Tooltip [/i]appears explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: Select the [i]Tooltip[/i] in order to open a web page providing help for the selected [i]Tool[/i].[br][br][b]Task[/b]: Find out how the [icon]/images/ggb/toolbar/mode_polygon.png[/icon] [i]Polygon [/i]tool works[br][list=1][*]Select the [img]https://wiki.geogebra.org/uploads/thumb/8/8a/Mode_polygon.svg/16px-Mode_polygon.svg.png[/img] [i]Polygon [/i]tool.[/*][*]Read the [i]Tooltip.[/i][/*][*]Figure out how to use this tool in order to create a triangle.[/*][/list]

Tools used in this Chapter

In this chapter, you are going to work with the following tools. Please make sure you know how to use them and try them out below prior to working on the following tasks.[br][u]Hints[/u]: [br][list][*]You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][/*][*]GeoGebra's [i]Tools[/i] are [b]organized in [i]Toolboxes[/i][/b], containing similar [i]Tools, [/i]or [i]Tools [/i]that generate the same type of new object. [/*][*]You can [b]open a [/b][i][b]Toolbox[/b] [/i]by clicking on a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][/*][*]When you select a [i]Tool[/i], a [b][i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][/*][*]If you want to [b]learn more about a [i]Tool[/i][/b], click on the [i]Tooltip[/i]. This opens a web page providing more detailed information for the selected [i]Tool[/i].[br][/*][/list][br][table][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/e/e3/Mode_join.svg/120px-Mode_join.svg.png[/icon][/td][td][b]Line[/b][br]Click twice in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] or on two already existing points in order to create a line through these points.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/c/c3/Mode_parallel.svg/120px-Mode_parallel.svg.png[/icon][/td][td][b]Parallel Line[/b][br]Click on an already existing line and a point in order to create a parallel line through this point.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/f/f3/Mode_intersect.svg/120px-Mode_intersect.svg.png[/icon][/td][td][b]Intersect[/b][br]Click on the intersection point of two objects to get this one intersection point. Successively click on both objects to get all intersection points.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/8/8a/Mode_polygon.svg/120px-Mode_polygon.svg.png[/icon][/td][td][b]Polygon[/b][br]Click in the [i][img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] Graphics View[/i] or on already existing points in order to create the vertices of a polygon. Connect the last and first vertex to close the polygon! [br][u]Note[/u]: Always connect vertices counterclockwise![/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/120px-Mode_move.svg.png[/icon][/td][td][b]Move[/b][br]Drag a free object to change its position.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/0/0c/Mode_segment.svg/120px-Mode_segment.svg.png[/icon][/td][td][b]Segment[/b][br]Click twice in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] or select two already existing points in order to create a segment between them.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/7/7e/Mode_orthogonal.svg/120px-Mode_orthogonal.svg.png[/icon][/td][td][b]Perpendicular Line[/b][br]Click on an already existing line and a point in order to create a perpendicular line through this point.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/1/14/Mode_pointonobject.svg/120px-Mode_pointonobject.svg.png[/icon][/td][td][b]Point on Object[/b][br]Click on an already existing object in order to create a point on this object.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/f/fb/Mode_circle2.svg/120px-Mode_circle2.svg.png[/icon][/td][td][b]Circle with Center through Point[br][/b]Your first click creates the center, while your second click determines the radius of the circle.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/2/25/Mode_showhideobject.svg/120px-Mode_showhideobject.svg.png[/icon][/td][td][b]Show / Hide Object[/b][br]Highlight all objects that should be hidden, then switch to another tool in order to apply the visibility changes![/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/3/30/Mode_angle.svg/120px-Mode_angle.svg.png[/icon][/td][td][b]Angle[/b][br]Click on the points in counterclockwise direction! GeoGebra always creates angles with mathematically positive orientation.[/td][/tr][/table]
Try it yourself...

The Navigation Bar and Construction Protocol

How to display the Navigation Bar
The [i]Navigation Bar[/i] allows you to review your construction step-by-step by using its buttons. [br][br][img]https://tube.geogebra.org/files/00/00/68/82/material-688219.png[/img]
Instructions
[list=1][*]Use the [img]https://wiki.geogebra.org/uploads/thumb/f/f6/Menu-button-open-menu.svg/16px-Menu-button-open-menu.svg.png[/img] [i]Menu[/i] button in order to open the menu.[br][/*][*]Select the [img]https://wiki.geogebra.org/uploads/thumb/6/67/Menu-view.svg/16px-Menu-view.svg.png[/img] [i]View[/i] menu.[br][/*][*]Check the option [i]Navigation Bar[/i].[br][/*][*]Close the menu using the [img]https://wiki.geogebra.org/uploads/thumb/f/f6/Menu-button-open-menu.svg/16px-Menu-button-open-menu.svg.png[/img] [i]Menu[/i] button again.[/*][/list]
Try it yourself...
How to display the Construction Protocol
The [img]https://wiki.geogebra.org/uploads/thumb/6/66/Menu_view_construction_protocol.svg/20px-Menu_view_construction_protocol.svg.png[/img] [i]Construction Protocol[/i] provides detailed Information about the construction steps.
Instructions
[list=1][*]Use the [img]https://wiki.geogebra.org/uploads/thumb/f/f6/Menu-button-open-menu.svg/16px-Menu-button-open-menu.svg.png[/img] [i]Menu[/i] button in order to open the menu.[br][/*][*]Select the [img]https://wiki.geogebra.org/uploads/thumb/6/67/Menu-view.svg/16px-Menu-view.svg.png[/img] [i]View[/i] menu.[br][/*][*]Check the option [img]https://wiki.geogebra.org/uploads/thumb/6/66/Menu_view_construction_protocol.svg/20px-Menu_view_construction_protocol.svg.png[/img] [i]Construction Protocol[/i].[br][/*][*]Close the menu using the [img]https://wiki.geogebra.org/uploads/thumb/f/f6/Menu-button-open-menu.svg/16px-Menu-button-open-menu.svg.png[/img] [i]Menu[/i] button again.[/*][/list]

Tools used in this Chapter

In this chapter, you are going to work with the following tools. Please make sure you know how to use them and try them out below prior to working on the following tasks.[br][u]Hints[/u]: [br][list][*]You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][/*][*]GeoGebra's [i]Tools[/i] are [b]organized in [i]Toolboxes[/i][/b], containing similar [i]Tools, [/i]or [i]Tools [/i]that generate the same type of new object. [/*][*]You can [b]open a [/b][i][b]Toolbox[/b] [/i]by clicking on a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][/*][*]When you select a [i]Tool[/i], a [b][i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][/*][*]If you want to [b]learn more about a [i]Tool[/i][/b], click on the [i]Tooltip[/i]. This opens a web page providing more detailed information for the selected [i]Tool[/i].[/*][/list][br][table][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/0/0c/Mode_segment.svg/120px-Mode_segment.svg.png[/icon][/td][td][b][/b][b]Segment[/b][br]Click twice in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] or select two already existing points in order to create a segment between them.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/7/7e/Mode_orthogonal.svg/120px-Mode_orthogonal.svg.png[/icon][/td][td][b]Perpendicular Line[/b][br]Click on an already existing line and a point in order to create a perpendicular line through this point.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/f/fb/Mode_circle2.svg/120px-Mode_circle2.svg.png[/icon][/td][td][b]Circle with Center through Point[br][/b]Your first click creates the center, while your second click determines the radius of the circle.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/f/f3/Mode_intersect.svg/120px-Mode_intersect.svg.png[/icon][/td][td][b]Intersect[/b][br]Click on the intersection point of two objects to get this one intersection point. Successively click on both objects to get all intersection points. [/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/8/8a/Mode_polygon.svg/120px-Mode_polygon.svg.png[/icon][/td][td][b]Polygon[/b][br]Click in the [i][img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] Graphics View[/i] or on already existing points in order to create the vertices of a polygon. Connect the last and first vertex to close the polygon! [br][u]Note[/u]: Always connect vertices counterclockwise![/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/2/25/Mode_showhideobject.svg/120px-Mode_showhideobject.svg.png[/icon][/td][td][b]Show / Hide Object[/b][br]Highlight all objects that should be hidden, then switch to another tool in order to apply the visibility changes.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/8/83/Mode_move.svg/120px-Mode_move.svg.png[/icon][/td][td][b]Move[/b][br]Drag a free object to change its position.[/td][/tr][tr][td][icon]https://wiki.geogebra.org/uploads/thumb/3/30/Mode_angle.svg/120px-Mode_angle.svg.png[/icon][/td][td][b]Angle[/b][br]Click on the points in counterclockwise direction. GeoGebra always creates angles with mathematically positive orientation (i.e. counterclockwise).[/td][/tr][tr][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_linebisector.png[/icon][/td][td][b]Perpendicular Bisector[/b][br]Click either on a segment or two points in order to create the perpendicular bisector.[/td][/tr][/table]
Try it yourself...

Take another GeoGebra Tour...

Introduction to GeoGebra
[size=100]The following Introductory Materials of the sequence "Introduction to GeoGebra" are available on the GeoGebra Materials Platform:[/size][list=1][*][size=100][url=https://ggbtu.be/bKTc2odjh]Basic Geometric Constructions[/url][br][/size][/*][*][size=100][url=https://ggbtu.be/bfPYPxVRv]Algebraic Input, Commands, and Functions[/url][/size][/*][*][size=100][url=http://ggbtu.be/bSoDHkCM7]Visualizing Mathematical Concepts[/url][/size][/*][/list]
The official GeoGebra Manual
[size=100]For further information please also see the [url=https://wiki.geogebra.org/en/Manual]Official GeoGebra Manual[/url].[/size]

Information