

A graphical proof of the Pythagorean Theorem
This graphical 'proof' of
the Pythagorean Theorem
starts with the
right triangle
below, which has sides of length a, b and c.
It demonstrates that
a^{2} + b^{2} = c^{2}, which is the Pythagorean Theorem.
It is not strictly a proof,
since it does not prove every step (for example it does not prove that the empty
squares really are squares). But
it does demonstrate the theorem in an interesting way.
Instructions Click on 'Next' to go through the proof one step at a time, or click on 'Run' to let it run without stopping.
The proof stepbystep
Step 1 
Make 3 copies of the original triangle and arrange the four triangles in a
square
as shown. The outer
square JKLM will remain fixed throughout the rest of the proof. 
Step 2 
Each side of the empty square in the middle has a length of c, and so has an area of
c^{2}. 
Step 3 
Rearrange the triangles as shown so that the empty space is now divided into two smaller squares. 
Step 4 
Notice that the top left empty square has each side equal to a, so its area is a^{2}. 
Step 5 
Notice also that the bottom right empty square has each side equal to b,
so its area is b^{2}. 
Step 6 
Done. We have rearranged the triangles inside a constantsize square.
The empty space we started with ( c^{2} ) must be equal to the sum of the two empty spaces at the end.
Therefore a^{2}+b^{2} = c^{2}
QED.

Other triangle topics
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Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
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