Basic Geometry with GeoGebra
GeoGebra is a fantastic dynamic geometry programme. It is free, interactive, and multi-platform. Its main goal is to help teach and learn mathematics. It covers all levels of education, from school to university. It includes manuals, guides, and video tutorials.
It is available on Windows, Mac OS, Linux, and every tablet platform — even as a Chrome Application.
Drawing lines and segments
Let’s start by drawing a simple line.
Please, observe that this applet works and that you can use it to follow these instructions without needing to install anything.
Then, you have to double click the central area again and, as a result, you will get two points (C, D) and a segment.
It is also possible to get the same result from the input field in the bottom panel. If you want to introduce points, just type: (6, 2), (4.5). Drawing lines is very simple, too. Let me illustrate with some examples: y = 2 * x + 3 or 3 * x-7 * y = 0.
Depending on your browser, you may need to install Java. If you are a Windows user just go to Java.com Follow these instructions to install Java In Ubuntu:
1 sudo apt-get purge openjdk* --1. Instalar Java 2 sudo add-apt-repository ppa:webupd8team/java 3 sudo apt-get update 4 sudo apt-get install oracle-java8-installer --2. Habilita Java en Firefox
Drawing angles, circles, tangents, and bisectors.
Let’s draw an angle and its bisector.
Check your results. Ask Geogebra to show you the angles between the angle’s bisector line and AB and AC.
Geogebra is a dynamic software application, so you can move points A, B, C, and all the angles, and the bisector will update automatically.
Click on the central area (A, it will be the centre of the circle), and then, click again on another point that will delimit its radius (B). If we wrote in the input field: Circle [A,7], we would get a circle with centre A and a radius of 7. If we have two points A and B, Circle [A,B] returns a circle with centre A passing through point B.
If we have a third point C, we can construct the tangent line to the circle passing through it. Just select the option Tangents in the menu Perpendicular line. First, click on the point C, and then, on the circle. We could have also written the command Tangent[C, c] where C is the point, and c the circle.