[b]Task[/b]: Construct a square by following the construction steps below. [table][tr id=kstep_1][td][size=100]1.[/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_segment.png[/icon][/size][/td][td][size=100]Select the [i]Segment [/i]tool. Click twice in the [i]Graphics View[/i] in order to create two points [i]A[/i] and [i]B[/i], and a segment between them. [/size][/td][/tr][tr id=kstep_2][td][size=100]2.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon][/size][/td][td][size=100]Activate the [i]Perpendicular Line[/i] tool. Create a line [i]b[/i] that is perpendicular to segment [i]AB[/i] and runs through point [i]B.[/i] [u]Hint[/u]: Select segment [i]AB[/i] and then point B in order to create the perpendicular line.[/size][/td][/tr][tr id=kstep_3][td][size=100]3. [/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Select the [i]Circle with Center through Point[/i] tool and construct a circle [i]c[/i] with center [i]B[/i] through point [i]A[/i]. [u]Hint[/u]: First, select point [i]B[/i] and then point [i]A[/i].[/size][/td][/tr][tr id=kstep_4][td][size=100]4.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Select the [i]Intersect[/i] tool. Intersect the perpendicular line [i]b[/i] with the circle [i]c[/i] to get the intersection point [i]C[/i]. [u]Hint[/u]: Click directly on the intersection of the line and the circle.[/size][/td][/tr][tr id=kstep_5][td][size=100]5.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon][/size][/td][td][size=100]Construct a perpendicular line [i]d[/i] to line [i]AB[/i] that runs through point [i]A[/i].[/size][/td][/tr][tr id=kstep_6][td][size=100]6.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100]Select the [i]Circle with Center through Point[/i] tool and construct a circle [i]e[/i] with center [i]A[/i] through point [i]B[/i].[/size][/td][/tr][tr id=kstep_7][td][size=100]7.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Create the intersection point D of the line [i]d[/i] and circle [i]e[/i]. [/size][/td][/tr][tr id=kstep_8][td][size=100]8.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/size][/td][td][size=100]Select the [i]Polygon [/i]tool. Create the square [i]ABCD[/i] by respectively selecting all four vertices[i].[/i] [u]Hint[/u]: To close the polygon, select the first vertex again.[/size][/td][/tr][tr][td][size=100]9.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Use the [i]Move[/i] tool in order to drag the vertices of the square and observe, how the construction adapts to your modifications.[/size][/td][/tr][tr id=minusAndPoints][td][/td][td][/td][td][/td][/tr][/table]
[b]Intermediate steps checking tools:[/b] [list] [*]kstep_1: Checks for an arbitrary segment [*]kstep_2: Checks for a perpendiculat line [*]kstep_3: Checks for a circle with center through point [*]kstep_4: Checks for an intersection point [*]kstep_5: Checks for two perpendicular lines [*]kstep_6: Checks for two circles [*]kstep_7: Checks for two intersection points [/list] [b]Final result checking tool[/b] [list][*]kstep_8: Created using tool Regular Polygon, checks for a square[/list] [b]Additional checking tools[/b] [list] [*]kstep_9: Checks for an arbitrary line [*]kstep_10: Checks for an arbitrary quadrilateral [/list]