Inverse Pythagorean Theorem

Date: 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!