In this GeoGebra tutorial, we use the Perpendicular Line and Parallel Line tools to construct a rectangle. The idea is to construct segment AB, construct two lines perpendicular to it, one passing through segment A and the other through segment B. Next, we will construct point on the line passing through B, then construct a line parallel to AB passing through C. The fourth intersection will be our point D. If you want to follow this construction step-by-step, click here to open GeoGebra on your browser.
|1. Open GeoGebra and select Geometry from the Perspective menu on the side bar.|
|2. To automatically show the labels of points and not the other objects, click the Options menu, click Labeling, then click New Points Only.|
|3. To construct a rectangle, select the Segment between Two Points tool and click two distinct places on the Graphics view to construct segment AB.|
|4. We construct two lines that are both perpendicular to AB, one passing through A and the other through B. To do this, click the Perpendicular Line tool, click point A and click the segment. To construct another line, click point B then click the segment. After these steps, your drawing should look like the one shown in Figure 1.|
|5. Next, we construct a point on the line passing through point B. To do this, click the New Point tool, and then click on the line passing through B.|
|6. Now, to create a line parallel to AB, passing through point C, click the Parallel line tool, click on point C and then click on the segment.
Your drawing should look like the one shown in Figure 2 after this step.
|7. Using the intersect tool, we construct the intersection of the line passing C (parallel to AB) and the line passing through A. To do this, click the Intersect Two Objects tool and click the two lines mentioned.|
|8. Now, we hide the three lines. To do this, click the Show/Hide Object tool and click the three lines. Notice that the lines are highlighted. Click Move tool to hide the lines.|
|9. Use the Segment between Two Points tool to connect the points to construct the rectangle.|
|10. Drag the points of the vertices of the rectangle. What do you observe?|