畢氐定理20pts!!!!!!!

(1) Proof by rearrangement
A proof by rearrangement is given by the illustration and the animation. In the illustration, the area of each large square is (a + b)². In both, the area of four identical triangles is removed. The remaining areas, a² + b² and c², are equal.

Remark:Elegant animation showing a proof by rearrangement is shown at the below website - http://upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pythagoras-2a.gif/200px-Pythagoras-2a.gif

(2) Algebraic proof
An algebraic variant of this proof is provided by the following reasoning. Looking at the illustration which is a large square with identical right triangles in its corners, the area of each of these four triangles is given by an angle corresponding with the side of length C.

The A-side angle and B-side angle of each of these triangles are complementary angles, so each of the angles of the blue area in the middle is a right angle, making this area a square with side length C. The area of this square is C^2. Thus the area of everything together is given by: 4x(AB/2)+C^2

However, as the large square has sides of length A + B, we can also calculate its area as (A + B)^2, which expands to A^2 + 2AB + B^2.

4x(AB/2)+C^2 = A^2 + 2AB + B^2
2AB+C^2 = A^2 + 2AB + B^2
C^2 = A^2 + B^2

Remark:A square created by aligning four right angle triangles and a large square is shown at the below website - http://upload.wikimedia.org/wikipedia/commons/thumb/2/26/Pythagproof.svg/180px-Pythagproof.svg.png

if a2+b2=c2
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then,abc is a right triangle

畢氐定理=a的2次方+b的2次方=c的2次方
24的2次方7的2次方=25的2次方
84的2次方+13的2次方=85的2次方

畢氐定理Pyth. thm.
多數係用黎計三角形斜邊既長度

畢氐定理的例子：
3^2 + 4^2 = 5^2
5^2 + 12^2 = 13^2