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Pitágoras: Teorema esencial

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Pitágoras: Teorema esencial

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Quiz sobre Pitágoras

Created by

Armando Ramirez
Armando Ramirez
Colombia

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Pitágoras: Teorema esencial
 

Pitágoras: Teorema esencialOnline version

Quiz sobre Pitágoras

by Armando Ramirez
1

¿Qué afirma el Teorema de Pitágoras?

2

Si c1=3 y c2=4, ¿cuál es 𝒽 en un triángulo rectángulo?

3

¿Qué tipo de triángulo se necesita para aplicar el Teorema de Pitágoras?

4

Si 𝒽=13, c1=5, ¿cuánto es c2?

5

¿Qué representa 𝒽 en el Teorema de Pitágoras?

6

¿Qué procedimiento utiliza Pitágoras para calcular un lado?

7

¿Cuál de estos triples pitagóricos es correcto?

8

Si c1=8 y c2=15, ¿cuánto es 𝒽?

9

¿Puede aplicarse el teorema a cualquier triángulo?

10

¿Qué pasaría si 𝒽^2 ≠ c1^2+c2^2 ?

Explicación

La hipotenusa al cuadrado equivale a la suma de los cuadrados de los otros dos lados.

𝒽^2=3^2+4^2 => 𝒽^2=9+16=25 => 𝒽=√25 por tanto 𝒽=5.

Solo en triángulos rectángulos se relacionan los lados con 𝒽^2=c1^2+c2^2.

𝒽^2= c1^2+c2^2 => 13^2 = 5^2+c2^2 => 169=25+c2^2 => 169-25=c2^2 => 144=c2^2 => √144=c2 => c2=12.

𝒽 es la hipotenusa, el lado opuesto al ángulo recto.

Se usa la relación de cuadrados para hallar el tercer lado (hipotenusa).

3-4-5 es un triple pitagórico clásico.

𝒽^2=8^2+15^2 => 𝒽^2=64+225 => 𝒽^2=289 => 𝒽=√289 => 𝒽=17.

Requiere un ángulo de 90°.

Para un triángulo rectángulo se debe cumplir 𝒽^2=c1^2+c2^2; de lo contrario no es un triángulo rectángulo.

 
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