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Teorema de pitagoras
El estudiante debe conocer que:
-
los ángulos interiores de un cuadrado son rectos
-
el área de un triángulo rectángulo es igual a semi promedio de la longitud de sus catetos.
-
El área de un cuadrado es igual al cuadrado de la medida de sus lados
Consideramos la figura
El área del cuadrado chico (blanco) es a2
El área del cuadrado grande (verde) es (c +b )2
Del álgebra sabemos que (c + b )2 = c2 + 2cb + b2
Cómo el área de cada triángulo viene dada por (bc)/2
entonces, la suma de las cuatro áreas es 4 (bc)/2 = 2bc
Podemos asegurar entonces que:
el área del cuadrado chico más el área de los triángulos es igual al área del cuadrado grande, es decir
a2 + 2bc = c2 + 2cb + b2
a2 = c2 + b2
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Enviado por: | Yorskio |
Idioma: | castellano |
País: | México |