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Using a ruler and compass only, it is possible to construct a square in any triangle so that one side of the square rests on one side of the triangle, and the other two vertices of the square touch the other two sides of the triangle:
Can you find a way to construct the square, for any triangle?
Can you explain why your method works?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.