Leonardo Da Vinci's Proof of the Pythagorean Theorem
The original right triangle (green) has legs a and b and hypoteneuse c.
The squares (blue and red) have sides a and b.
Cut apart and reassemble the pieces of the two squares (with sides a and b)
to make a square with side c.
Do this by following these steps:
- Cut the squares on a and b in half diagonally with a single line.
- Reflect one half in a line perpendicular to the cutting line.
- Cut triangles congruent to the original triangle off the ends and
rotate them into the gaps.
In a right triangle with legs a and b and hypoteneuse c,
| the area of the square on a | a2
|
| added to the area of the square on b | + b2
|
| is the area of the square on c. | = c2
|
Geometer's Sketchpad sketch by Susan Addington, based on "Leonardo da Pythagoras", by D. Bennett
This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1997 by Key Curriculum Press, Inc. All rights reserved. Portions of this work are being funded by the National Science Foundation (awards DMI 9561674 & 9623018).
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