# A problem based on the Finsler-Hadwiger theorem

## The Problem

If you build squares off 2 sides of any triangle, you’re guaranteed a hidden 45-45-90 triangle.

## Exploring the solution involving successive tranformations of a point.

M' is the rotation of the point M around D by 90°(CCW). M'' is the rotation of the point M' around the point E by 90°(CCW). Rotation of this point M'' around the point F by 180° brings it back to the point M.
You can see this for yourself by moving the point M in the applet.
What if the point M coincides with the point A? What if the point M coincides with the point D? Use the given buttons to see.
To change the sizes of the two squares move the blue coloured points.

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