Prove the converse Pythagorean theorem: If a,b,c> 0 and a + b = c then the...

 

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Prove the converse Pythagorean theorem: If a,b,c> 0 and a² + b² = c²₂ then the triangle with sides a,b,c is right-angled. How can we be sure that lengths a,b,c> 0 with a² + b² = c² actually fit together to make a triangle? (Hint: Show that a+b>c.) Prove the converse Pythagorean theorem: If a,b,c> 0 and a² + b² = c²₂ then the triangle with sides a,b,c is right-angled. How can we be sure that lengths a,b,c> 0 with a² + b² = c² actually fit together to make a triangle? (Hint: Show that a+b>c.)

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To prove the converse Pythagorean theorem we need to show that if a b and c are positive real number... View the full answer