GeoGebra Essentials 6 – Sliders and Rhombuses

This is the sixth tutorial in the GeoGebra Essentials Series. If you are not familiar with GeoGebra, you may want to read the Introduction to GeoGebra post and earlier tutorials. They contain the pre-requisites of this tutorial.

In the tutorial below, menu commands, located in the menu bar, are in brown bold text, and submenus are denoted by the > symbol. For example, Options>Labeling> New Points Only means, click the Options menu, choose Labeling from the list, then select New Points Only. The tool texts are colored orange. For example, New Pointmeans the new point tool.

In this tutorial, we construct a rhombus using the slider tool.  A slider (see figure below) is a dynamic graphical representation of a number.  We have three types of sliders – number, angle and integer.  The angle and number sliders are shown below. Slider s is the side length of the rhombus ABCB’. Slider t on the other hand is the measure of angle A.

In doing the tutorial, we  learn the following:

  • Use the tools we have discussed in previous tutorials – Segment tool, Parallel Line tool,and Intersect tool
  • Learn how to use new tools including Angle with Given Size and Segment with Given Length from Point .
1. Open GeoGebra. Select Geometry from the Perspective panels in the Sidebar. We automatically label  points by selecting Options>Labeling> New Points Only from the menu bar.
2. First, we construct two sliders s and t. Slider s will be the side length of the rhombus, while slider t will be the angle measure of one of the interior angles. To construct slider s, select the Slider tool, and then click on the Graphics view. This will display the slider dialog box as shown in Figure 1.
3. In the Slider dialog box, select the Number option, type s in the Name box, set the Min length to 0, set the Max length to 5, and leave the interval to 0.1. Click the Apply button to finish. Adjust the position of the slider if necessary by dragging it (don’t drag the circle).

4. We now create segment AB with length s. To do this, select the Segment with Fixed Length tool, then click a vacant space on the Graphics view. This displays the Segment with Fixed Length dialog box as shown in Figure 2. Type s in the length text box, and then click the OK button.

Figure 2

5. Now, move slider s and observe what happens to the segment.
6. We now construct angle slider t. To do this, select the Slider tool, and then click a vacant space in the Graphics view to display the Slider dialog box.
7. In the Slider dialog box, select the Angle option, replace the angle Name with t, leave the min box to 0 degrees, replace the max box with 180 (do not delete the degree sign), leave the interval to 1 degree, and then click the Apply button to finish.
8. Next, we construct angle BAB’ which will be an interior angle of the rhombus. Select the Angle with Given Size tool, click point B, and then click point A, to display the Angle with Given Size dialog box*.
9. In the Angle with Given Size dialog box, replace the angle measure with t, leave the rotating option to counterclockwise, and then click the OK button.
10.  Use the Segment tool and construct AB’. Your drawing should look like the one shown in Figure 3.

Figure 3

11.  Now, using the Parallel Line tool, construct a line parallel to AB and passing through B’. Similarly, construct a line parallel to AB’ and passing through B.
12.  Using the Intersect tool, determine the intersection of the two lines. Your drawing should look like the one shown in Figure 4.

Figure 4

13.  Hide the two lines by right clicking them, and then clicking the Show Object option from the context menu.
14.  Connect B’C and BC using the Segment  tool.
15.  Use the sliders to change the shape of the rhombus. Explain why the figure is a rhombus.
16.  Save your file by clicking File>Save on the menu bar. Name your file as essentials6

Notes:

*B’ is the rotation B about A t degrees counterclockwise.

Last Update: 16 December 2015 (GeoGebra 5.0)

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  1. Pingback: Dica de blog: Matemática e Multimídia | André Machado

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