Geometry for Elementary School/Pythagorean theorem

Some impossible constructions A proof of irrationality alt=Pythagorean Theorem|thumb|The area of the squares that a and b make are equal to the area of the square that c makes In this chapter, we will discuss the Pythagorean theorem. It is used to find the side lengths of a right triangles. It says: In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse). This means that if is a right triangle, the length of the hypotenuse, c, squared equals the sum of a squared plus b squared. Or: Here's an example: In a right-angled triangle, a=5cm and b=12cm, so what is c? If c is not larger than a or b, your answer is incorrect. There may be a number of reasons that your answer is incorrect. The first is that you have calculated the sums wrong, the second is that the triangle you are trying to find the hypotenuse of is not a right angled triangle or the third is you have mixed up the measurements. There may be more finer points to having a wrong answer but the three stated are the most common. Exercise Write about Pythagorean Theorem and its use to prove that is an irrational number. it:Geometria per scuola elementare/Il Teorema di Pitagora