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So I have that squares A and B are congruent and one vertex of B is at the center of A. The question is what is the ratio of the shaded area to the area of square A. My question is if two square are congruent then must their sides also be the same?

Gamecocks99
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That is correct, if two shapes are congruent then you can take each side and each angle in succession and know that the angles are congruent and the sides are the same length. This does not mean that the two shapes have the same orientation or position however.

abiessu
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    Thats what I was thinking especially since one of the squares in this problem is rotated around the center of the other one, I just wanted to double check that if square A had length a then square B must also have side length a before I assumed it in my proof. Appreciate it! – Gamecocks99 Oct 20 '13 at 21:21