Learn how to rotate a polygon by a given angle using a slider and enhance your construction by hiding all [i]Auxiliary Objects[/i] in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i].

[table][tr][td]1.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Create an arbitrary triangle [i]ABC[/i] in the first quadrant placing the vertices on grid points.[/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_point.png[/icon][/td][td]Create a new point [i]D[/i] at the origin of the coordinate system.[/td][/tr][tr][td]3.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/8/84/Menu-edit-rename.svg/32px-Menu-edit-rename.svg.png[/icon][/td][td]Rename the point [i]D[/i] to [i]O[/i].[br][b]Hint[/b]: Select point [i]D[/i] and just type [code]O[/code] to open the [i]Rename [/i]dialog.[/td][/tr][tr][td]4.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_slider.png[/icon][/td][td]Create a slider for angle [i]α[/i].[br][b]Hint:[/b] In the [i]Slider[/i] dialog window, check [i]Angle[/i] and set the [i]Increment[/i] to 90 ̊. Make sure you don’t delete the ̊ symbol.[/td][/tr][tr][td]5.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_rotatebyangle.png[/icon][/td][td]Use the [i]Rotate around Point[/i] tool to rotate triangle [i]ABC[/i] around point [i]O[/i] by angle [i]α[/i].[br][/td][/tr][tr][td][br][/td][td][br][/td][td][b]Hints:[/b] Activate the tool and select the triangle before you select the center of rotation. In the appearing dialog, enter [i]α[/i] as the angle through the [img]https://wiki.geogebra.org/uploads/thumb/c/ce/Baseline-keyboard-24px.svg/24px-Baseline-keyboard-24px.svg.png[/img] [i]Virtual Keyboard[/i] and choose [i]counter clockwise[/i] rotation.[/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/td][td]Create segments [i]AO[/i] and [i]A’O[/i][/td][/tr][tr][td]7.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon][/td][td]Create angle [i]AOA[/i]’.[br][b]Hint:[/b] Select the points in counter clockwise order.[/td][/tr][tr][td]8.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_showhidelabel.png[/icon][br][/td][td]Hide the label of angle [i]AOA[/i]’.[br][/td][/tr][tr][td]9.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Move the slider and explore the image of the triangle.[br][/td][/tr][/table]

You will now learn how to ‘tidy up’ the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] by defining some objects as [i]Auxiliary Objects[/i] and hiding their algebraic representation. Thus, your students will be able to explore the coordinates of the initial points and their images in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] without being distracted by the algebraic representations of the other objects used in this construction.[br][br][table][tr][td]1.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/6/67/Menu-view.svg/120px-Menu-view.svg.png[/icon][/td][td]Show the [i][img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img][/i] [i]Algebra View [/i]using the [i]View [/i]menu[i].[/i][/td][/tr][tr][td]2.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td]Select all segments in the [i]Algebra View[/i].[br][b]Hint:[/b] Click on the heading [i]Segment[/i] in order to select all segments at the same time.[/td][/tr][tr][td]3.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/3/30/Menu-options.svg/120px-Menu-options.svg.png[/icon][/td][td]Open the [i]Settings[/i] for the segments using the [img]https://wiki.geogebra.org/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/16px-Stylingbar_icon_graphics.svg.png[/img] [i]Style Bar[/i] and check [i]Auxiliary Object[/i] on tab [i]Basic[/i].[/td][/tr][tr][td]4.[/td][td][/td][td]Repeat the last two steps for the triangles, angles and point [i]O[/i] at the origin.[br][b]Hint:[/b] The [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] now only contains points [i]A, B,[/i] and [i]C[/i] as well as their images [i]A’, B’,[/i] and [i]C’[/i].[/td][/tr][/table][b]Note:[/b] You can now show or hide the [i]Auxiliary Objects[/i] by toggling the [img]https://wiki.geogebra.org/uploads/thumb/f/f6/Stylingbar_algebraview_auxiliary_objects.svg/16px-Stylingbar_algebraview_auxiliary_objects.svg.png[/img] [i]Auxiliary Objects[/i] button in [img]https://wiki.geogebra.org/uploads/thumb/6/6c/Stylingbar_icon_algebra.svg/16px-Stylingbar_icon_algebra.svg.png[/img] [i]Algebra View Style Bar[/i].