Proving the Pythagorean theorem - MathML 编辑

We will now prove the Pythagorean theorem:

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

i.e, If a and b are the legs and c is the hypotenuse then${\mathrm{ \; a}}^2+b^2=c^2$.

Proof:  We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: $\begin{array}{rcl}{(a+b)}^2& =& c^2+4\cdot \left(\frac{1}{2}ab\right) \; \; \; \; \; \; \; \; \; \; \; \; \; \\ a^2+2ab+b^2& =& c^2+2ab\\ \\ a^2+b^2& =& c^2\end{array}$