Inverse Pythagorean TheoremDate: 05/10/2001 at 22:09:20 From: Julie Subject: Math How can you tell a triangle is a right triangle without looking at the triangle and just how long the sides are? Date: 05/11/2001 at 11:42:14 From: Doctor Rick Subject: Re: Math Hi, Julie. What you're looking for is the inverse Pythagorean theorem. The (regular) Pythagorean theorem says that if a triangle is a right triangle, then the square of its longest side (the hypotenuse) is equal to the sum of the squares of the other two sides. The inverse Pythagorean theorem says that, if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 05/11/2001 at 11:47:12 From: Doctor Twe Subject: Re: Math Hi Julie - thanks for writing to Dr. Math. Pythagoras' theorem says that if a triangle is a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides; that is: C^2 = A^2 + B^2 The converse is also true; if the square of the hypotenuse is equal to the sum of the squares of the other two sides, then the triangle must be a right triangle. So to check whether a triangle of known sidelengths is a right triangle, square each side length; if the largest number is equal to the sum of the other two, the triangle must be a right triangle. I hope this helps! If you have any more questions, write back! - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ Date: 05/12/2001 at 09:30:24 From: Julie Subject: Re: Math Thank you! |
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