Then put a second triangle below the first such that side a
is an extension of the other triangles b side.
Next connect the end of side a at the top with side b on the
bottom to create the trapezoid.
Remembering the formula for the area of a trapezoid to be
the formula for the area of this trapezoid will be . This area will be the same as the sum of the areas of the three triangles that are located inside the trapezoid
Setting these equal you get
Simplifying both sides you come to
By multiplying both sides by two it becomes
Then subtracting both sides by 2ab the end result is which is the Pythagorean Theorem.
Another proof of this theorem is the DaVinci proof of using areas and cutting and pasting them to show equal areas. Click here.
For more ways of looking at the Pythagorean Theorem, try these:
Leonardo da Pythagoras
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