GeoGebra Tutorial: Using the Perpendicular Line and the Point on Object Tools
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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.
Guillermo Bautista, Created with GeoGebra
Guillermo Bautista, Created with GeoGebra
Snapshot
2.) Move slider p to the extreme right. What is the area of the figure formed in terms of a and b?
3.) What can you say about the area of the square in Question 1 and the area of the figure in Question 2?
4.) What equation can you form using the areas of these squares?
To construct a triangle congruent to triangle ABC, move the slider to the right. To see the construction steps, move the slider slowly to the extreme right.
The applet above shows that if the three corresponding sides of two triangles are congruent, then the two triangles are congruent.