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Using a ruler and compass only it is possible to fit a square into 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

 

How is this possible?

Prove why this works.

It is easy to draw a square ABCD with BC on the base PR of the triangle and the vertex D on the side PQ

 

Small square drawn in left-hand corner of the triangle

 

What happens to the point A as you enlarge the square? The interactivity may help.

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