Teorema de Pitágoras

      The Pythagorean theorem is considered one of the major discoveries of mathematics, it describes a relationship in the triangle. Remember that the triangle can be identified by the existence of a right angle, ie, measuring 90 °. The triangle consists of two peccaries and the hypotenuse, which is the largest segment of the triangle and is located opposite the right angle. Note: 

Cathetus: a and b 
Hypotenuse c 

The theorem says that: "the sum of the squares of the legs equals the square of the hypotenuse." 

a² + b² = c²

example 1 
Calculate the value of the unknown segment in the triangle below. 

x² = 9² + 12²

x² = 81 + 144

x² = 225

√x² = √225

x = 15

  It was through the Pythagorean theorem that the concepts and definitions of irrational numbers began to be introduced in Mathematics. The first to emerge was irrational √ 2, which appeared the hypotenuse of a right triangle with the other two sides measuring 1 See be calculated.: 

            

x² = 1² + 1²

x² = 1 + 1

x² = 2

√x² = √2

x = √2

√2 = 1,414213562373....

example 2
Calculate the value of the collared peccary in the rectangle triangle below:

x² + 20² = 25²

x² + 400 = 625

x² = 625 – 400

x² = 225

√x² = √225

x = 15

Suppose that 1 or Cateto Cateto A, was equal to 8 cm and the peccary or Cateto 2 B, is equal to 6 cm.Qual is the value of the hypotenuse? 

        

Solution: 

x² = 8²+6²

x² = 36+64

x = √100 = 10

x= 10 cm 

   Observation:


He knows the legs, but he does not know the hipotenusa.Então this calculation to find out the result of x ², which in this case is 10 cm.