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Nice Geometry Problem

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Edited by Richard Walker, Thursday, 6 Apr 2023, 18:04


Suppose we take a rectangle and erect equilateral triangles on two of its side, as shown in Fig. 1. Show that pointsC, E and B are the vertices of an equilateral triangle.

Here is my proof: If we draw in the sides of the triangle (Fig. 2) we can see triangles DCE, BEF and DFA all have

a side of length | and one of length ||
an angle of 150 degrees included between those sides.

Consequently the three triangles are all congruent (the same as on another) and DE = EF = FD, so DEF is equilateral as required.
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