GeoGebra Essentials 2 – Constructing a Rectangle

This is the second tutorial in the GeoGebra Essentials Series. If this is your first time to use GeoGebra, it is important that you read the Introduction to GeoGebra post. It is also important to read the GeoGebra Essentials 1. This tutorial is just a repeat of the GeoGebra Basic Construction 5, but I have put a more thorough discussion on free, semi-free and independent objects.

In the tutorial below, menu commands, located in the menu bar, are in green bold text, and the submenus are denoted by the > symbol. For example, Options>Labeling>New Points Only means you have to click the Options menu, choose Labeling from the list, then New Points Only. The tool texts are colored light red. For example, New Point means, the New Point tool.

In this tutorial, we  create a rectangle using the segment tools, the parallel line tool, and perpendicular line tool.  We learn how to measure the length of segments and angles. The output is of this tutorial is shown below.

In doing the tutorial, you will learn the following:

  • use the previous tools we have discussed in GeoGebra Essentials 1 New Point tool, Segment Tool and Intersect Two Object tools
  • how to use new tools including Parallel Line tool, Perpendicular Line tool, Show/Hide Objects tool
  • the difference between free objects and independent objects, and discuss about semi independent objects.
1. Open GeoGebra. Select Geometry from the Perspective panel located in the sidebar. Label all the created objects automatically by selecting Options>Labeling>All New Objects from the menu bar.
2. To construct segment AB, select the Segment between Two Points tool, and click two different locations on the Graphics View1. This is segment a.
3. Next, we construct two lines which are both perpendicular to segment a and passing through the two endpoints. First we construct a line passing through point A perpendicular to segment a. To do this, select the Perpendicular Line tool, click on segment a and then click on point A. This creates line b. Using the previous step, construct a line perpendicular to segment a and passing through point B. This is to be line c.
4. Now select the Move tool and drag the objects. Which of the objects can or cannot be moved? Can you explain why?
5. Next, we create a point on line b. To do this, select the New Point tool and then click on line b. This will be point C. Notice that the color of point C is slightly lighter compared to the color of the other points. Use the Move tool to drag point C. What do you observe?2
6. Next, we construct a line passing through point C and parallel to segment a. To do this, select the Parallel line tool, click on segment a and click  on point C. This will produce line d.
7. We now create the intersection between line c and line d. To do this, select the Intersect Two Objects tool, and then click on the intersection of the two lines.  This will produce point D.   Now, try dragging the objects. What do you observe?

8. Now, we hide lines b, c, and d. To do this, right click each object and click Show Object from the pop-up menu.3.

9. Now, connect the points using the Segment between Two Points tool to construct rectangle ABDC. Hide the labels of the segments by right-clicking each of them and selecting Show label from pop-up menu. This completes the rectangle.
10.  Now, save your file by clicking File>Save on the menu bar. Name your file as essentials2. View the output file and answer the embedded questions.


1Notice that aside from the labels of the points namely A and B, GeoGebra also named the segment a. This is because each object in GeoGebra is treated differently. The points are different from the segment.  All objects are shown on the Algebra view. You also probably notice that the segment is named in small letter and the points are named in capital letters.

2Be sure that point C is on line b. If you can drag point C outside line b, delete the point and repeat the construction.

3Objects can also be shown/hidden using the Algebra window by clicking the circle next to the objects. The empty circles are hidden objects while the colored circles are displayed objects.

GeoGebra algebra window

Semi-Free Objects

In GeoGebra Essentials 1, we have learned about dependent objects and free mathematical objects. We have learned that free objects do not depend on other objects and hence can be moved anywhere on the Graphics view, while independent objects cannot be moved without dragging the objects they depend on.  In the construction above, points A and B are free objects; lines b, line c and point D are dependent objects.

But let us look at point C. Point C is dependent object (dependent on the line), yet we can move it along line a. We will call this object semi-dependent or semi-free object. From here we have three types of objects:

  1. Free Objects – Objects which do not depend on any object; can be moved anywhere on the Graphics view.
  2. Semi-free Objects – Objects which depend on another object; can be moved on the drawing pad, but with restriction
  3. Dependent objects – Objects which depends usually on more than one object; cannot be moved without moving the object it depends on.

Last Update: October 14, 2015

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