Wednesday, November 21, 2012

GeoGebra Tutorial: Using the Perpendicular Line and the Point on Object Tools

In this tutorial, we use GeoGebra to explore the minimum sum of the distances of a point on the interior of a triangle to its sides. We learn how to use the Point on Object tool and the Perpendicular Line tool. We also learn how to compute using the Input bar. The final output of this tutorial is shown in the following applet.
This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
Steps in Creating the Applet

Thursday, November 15, 2012

Circumcircle and Circumcenter

Click the check boxes and move the vertices of the triangle to explore. What do you observe?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
In any triangle, a circle called circumcircle maybe drawn that passes through its vertices. The center of the circumcircle is called the circumcenter. The perpendicular bisector of the three sides of any triangle passes through its circumcenter.




Wednesday, November 7, 2012

Napoleon's Theorem

In the applet below, ABC is a triangle whose sides are also sides of equilateral triangles that contain the green line segments. Points P, Q, and R are centroids of the equilateral triangles.  

1) What do you observe about the figure?
2) Move points A, B, and C. Are your observations still the same?


This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

The Napoleon theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those triangles themselves form an equilateral triangle.