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Squirty

Age 14 to 16 Challenge Level:

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:

 

Square inscribed in a triangle

 

Can you find a way to construct the square, for any triangle?
Can you explain why your method works?