Presented By: Alexander Sarkissian. Pythagoras’s Theorem First we will start with the common...
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Transcript of Presented By: Alexander Sarkissian. Pythagoras’s Theorem First we will start with the common...
Presented By:
Alexander Sarkissian
Pythagoras’s Theorem
First we will start with the common right triangle.
Side a= Adjacent side
Side b= Opposite side
Side c= Hypotenuse
We start out with four right triangles.Three of these have been rotated 90o, 180o, and 270o.
Each has an area of ab/2
Pythagoras’s Theorem
Let's put them together without additional rotations so that they form a square with side c.
Pythagoras’s Theorem
The square has a square hole with the side (a-b). Summing up its area (a-b)2 and 2ab, the area of the four triangles is (4·ab/2).
Formula c2 = (a-b)2+2ab = a2-2ab+b2+2ab=
a2+b2 Thus we simplify the equation and
end up with a²+b²=c²
The End
Sources: http://www.cut-the-knot.org/pythagoras/index.shtml