In the applet below,

1) What do you observe about the figure?

2) Move points

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.

*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?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.

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