Lesson PROOF of Pythagorean Theorem

Source code of 'PROOF of Pythagorean Theorem'

This Lesson (PROOF of Pythagorean Theorem) was created by by ichudov(507)

: View Source, Show
About ichudov: I am not a paid tutor, I am the owner of this web site!

nobreak
<TABLE> 
<TR> 
<TD> 
<IMG SRC=pyth.jpg> 
</TD> 
<TD> 
See also: <A HREF=http://en.wikipedia.org/wiki/Pythagorean_theorem>the Wikipedia article on the Pythagorean_theorem</A>.
<BR> 
Pythagorean theorem was proven by an ancient Greek named <A HREF=Pythagoras.wikipedia>Pythagoras</A>, and says that 
for a right triangle with legs A and B, and hypotenuse C<BR> 
<CENTER>
  {{{A^2 + B^2 = C^2}}},<BR>
  {{{C = sqrt( A^2 + B^2 )}}},<BR> 
  {{{A = sqrt( C^2 - B^2 )}}}.<BR>
 
</CENTER> 
</TD> 
</TR> 
</TABLE> 
 
<TABLE><TR> 
 
 
<TD> 
 
<IMG SRC=pythprf.gif> 
</TD> 
 
<TD>To the left is an animated proof of the Pythagorean Theorem. Starting with a 
right triangle and squares on each side, the middle size square is cut 
into congruent quadrilaterals (the cuts through the center and 
parallel to the sides of the biggest square). Then the quadrilaterals 
are hinged and rotated and shifted to the big square. Finally the 
smallest square is translated to cover the remaining middle part of 
the biggest square. A perfect fit! Thus the sum of the squares on the 
smaller two sides equals the square on the biggest side. 
<HR> 
 
<B>What this means in plain language</B>: 
 
<P>As you know, the area of a 
square is the length of its side, multiplied by itsemf (squared). For 
instance, the area of a square room that is 10 by 10 feet is 10 
multiplied by 10, that is, 100 square feet.</P> 
 
<P> What this animated proof says is this: take a square whose side is 
the same as the hypothenuse (green square). You can take <B>scissors</B> and cut this 
square into pieces that can be REASSEMBLED to become two 
squares. These two squares would be with the sides of the same length 
as the sides of the right triangle. 
 
</P> 
 
<P>Because cutting the big square with scissors and reassembling it into smaller pieces did not change the total \
area of the piece of paper, we now know that the area of the big square is the sum of areas of the small squares,\
 or 
 
 {{{A^2 + B^2 = C^2}}}<BR>
 
</TD> 
  
</TR></TABLE>

For in depth treatment of this wonderful theorem and various proofs, go to 
<A HREF=http://mathworld.wolfram.com/PythagoreanTheorem.html TARGET=_new>MathWorld</A>, 
or see these lessons <A HREF=http://www.algebra.com/algebra/homework/Pythagorean-theorem/The-Pythagorean-Theorem.lesson>The Pythagorean Theorem</A> and

<A HREF=http://www.algebra.com/algebra/homework/Pythagorean-theorem/More-proofs-of-the-Pythagorean-Theorem.lesson>More proofs of the Pythagorean Theorem</A> in the current module.