Create a parallelogram and change it by dragging the vertices of the figure. Explore how the values of the sides and angles are changing. [br][br]Explore the construction and learn how to discover properties of parallelograms with [url=https://www.geogebra.org/geometry]GeoGebra Geometry[/url]. Then try it yourself by following the instructions below.[br]

[b]Note:[/b] If you're using the Mobile App make sure that the chosen [i]Labeling[/i] option is [i]New Points Only[/i]. You can change this by going to the [i]Settings [/i]in the app's menu and then selecting [i]General.[/i][br][br][table][tr][td]1.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/td][td]Select the [i]Line[/i] tool and create a line [i]AB[/i] by clicking twice in the [i]Graphics View[/i].[/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/td][td]Create a line [i]BC[/i] using the [i]Line[/i] tool again.[br][b]Hint:[/b] Select point [i]B[/i] and then click in the [i]Graphics View[/i] to create point [i]C[/i].[/td][/tr][tr][td]3.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_parallel.png[/icon][/td][td]Activate the [i]Parallel Line[/i] tool and create a parallel line to line [i]AB[/i] through point [i]C[/i].[br][b]Hint:[/b] Select the line [i]AB[/i] and then point [i]C[/i].[/td][/tr][tr][td]4.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_parallel.png[/icon][/td][td]Create a parallel line to line [i]BC[/i] through point [i]A[/i] using the [i]Parallel Line[/i] tool again.[/td][/tr][tr][td]5.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Select the [i]Intersect[/i] tool and create the intersection point [i]D[/i] of the two lines.[br][b]Hint:[/b] Click directly on the intersection point.[/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Activate the [i]Polygon[/i] tool and create the parallelogram [i]ABCD[/i] by successively selecting all the vertices.[br][b]Hint:[/b] To close your polygon, select the first point again.[/td][/tr][tr][td]7.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_showhideobject.png[/icon][/td][td]Select the [i]Show / Hide Object[/i] tool and hide the auxiliary lines by selecting the lines.[br][/td][/tr][tr][td]8.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_showhidelabel.png[/icon][/td][td]Select a segment using the [i]Move [/i]tool[i] [/i]and select [i]Show Value[/i]. Repeat this for all sides of the parallelogram.[br][b]Note:[/b] In the Mobile App select the [i]More [/i]button, then [i]Set caption style[/i] and select [i]Value[/i].[/td][/tr][tr][td]9.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_angle.png[/icon][/td][td]Display the values of the angles by selecting the [i]Angle[/i] tool and selecting the parallelogram.[/td][/tr][tr][td]10.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Select the [i]Move[/i] tool and explore the properties of your construction.[/td][/tr][/table]

[table][tr][td]11.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_segment.png[/icon][/td][td]Construct the diagonals of the parallelogram using the [i]Segment[/i] tool. For the first diagonal select point [i]A [/i]and then point C[i] [/i]and for the second diagonal select point [i]B [/i]and then point [i]D[/i]. [/td][/tr][tr][td]12.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Create the intersection point of the diagonals using the [i]Intersect [/i]tool.[/td][/tr][tr][td]13.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_distance.png[/icon][/td][td]Select the [i]Distance or Length[/i] tool and select each segment of the vertices [i]A[/i], [i]B[/i], [i]C, [/i][i]D[/i] and the intersection point [i]E[/i] of the diagonals.[br][b]Hint:[/b][i] [/i]Select point [i]A[/i] and then point [i]E[/i]. Repeat this for points [i]B[/i], [i]C[/i] and [i]D[/i].[/td][/tr][tr][td]14.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_slope.png[/icon][/td][td]Select the [i]Slope [/i]tool and select all four sides of the parallelogram.[/td][/tr][tr][td]15.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Explore your construction using the [i]Move[/i] tool.[/td][/tr][/table]