Create an applet that illustrates the construction steps for a triangle whose three side lengths [i]a[/i] , [i]b[/i] and [i]c[/i] are given. Additionally, this applet will allow you to discover triangle inequalities.[br][br][b]Note:[/b] The triangle inequalities [i]a + b > c[/i], [i]b + c > a[/i] and [i]a + c > b[/i] state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.

[table][tr][td]1.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_slider.png[/icon][/td][td]Create sliders [i]a, b[/i] and [i]c[/i] for the side lengths of the triangle with an interval from 0 to 10 and [i]Increment [/i]0.5 each.[/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Set the slider values to [i]a = 8[/i], [i]b = 6.5[/i] and [i]c = 10[/i].[/td][/tr][tr][td]3.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segmentfixed.png[/icon][/td][td]Create segment [i]f[/i] with given length [i]c[/i].[br][b]Hint:[/b] Points [i]A[/i] and [i]B[/i] are the endpoints of the segment.[/td][/tr][tr][td]4.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_circlepointradius.png[/icon][/td][td]Create a circle [i]d[/i] with center [i]A[/i] and radius [i]b[/i].[/td][/tr][tr][td]5.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_circlepointradius.png[/icon][/td][td]Create a circle [i]e [/i]with center [i]B[/i] and radius[i] a[/i]. [/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Construct the intersection point [i]C[/i] of the two circles [i]e[/i] and [i]f[/i].[/td][/tr][tr][td]7.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Create the triangle [i]ABC[/i].[/td][/tr][tr][td]8.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon][/td][td]Create interior angles [math]\alpha[/math], [math]\beta[/math] and [math]\gamma[/math] of triangle [i]ABC.[/i][/td][/tr][/table]

[table][tr][td]9.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_pointonobject.png[/icon][/td][td]Create a point [i]D[/i] on circle [i]d[/i].[br][/td][/tr][tr][td]10.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/td][td]Create segment [i]g[/i] between the points [i]A[/i] and [i]D[/i].[br][/td][/tr][tr][td]11.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_midpoint.png[/icon][/td][td]Construct the midpoint [i]E[/i] of segment [i]g[/i].[/td][/tr][tr][td]12.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_text.png[/icon][/td][td]Enter [i]text1:[/i] b and attach it to point [i]E[/i].[br][b]Hint: [/b]After selecting the [i]Text[/i] tool, click on point [i]E[/i]. Open [i]Advanced [/i]and select[i] b [/i]from the [img]https://www.geogebra.org/wiki/uploads/thumb/f/f1/Worksheet_icon_applet.svg/16px-Worksheet_icon_applet.svg.png[/img] [i]Objects [/i]tab. [br][/td][/tr][tr][td]13.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_pointonobject.png[/icon][br][/td][td]Create a point [i]F[/i] on circle [i]e[/i].[br][/td][/tr][tr][td]14.[/td][td][icon]/images/ggb/toolbar/mode_segment.png[/icon][br][/td][td]Create segment [i]h[/i] between the points [i]B[/i] and [i]F[/i].[/td][/tr][tr][td]15.[/td][td][icon]/images/ggb/toolbar/mode_mirroratpoint.png[/icon][/td][td]Construct the midpoint [i]G[/i] of segment [i]h[/i].[/td][/tr][tr][td]16.[/td][td][icon]/images/ggb/toolbar/mode_text.png[/icon][br][/td][td]Enter [i]text2:[/i] a and attach it to point [i]G[/i].[/td][/tr][tr][td]17.[br][/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_showhideobject.png[/icon][br][/td][td]Hide points [i]D[/i], [i]E[/i], [i]F[/i] and [i]G[/i] by using the [i]Show / Hide Object[/i] tool.[br][/td][/tr][tr][td]18.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/d/db/Stylingbar_icon_graphics.svg/32px-Stylingbar_icon_graphics.svg.png[/img][/td][td]Enhance your construction by using the [i]Style Bar[/i] and match colors of corresponding objects.[/td][/tr][/table]