The Pythagorean theorem states that in aright angle triangle \ \

the square of a hypotenuse plus \ \

The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse.

Draw a square and inscribe a small tilted square inside it. \ \

Observe the figure, \ \

Whole figure is divided into four triangles and a square. \ \

Side of the outer square is .

Find the area of the big square. \ \

Area of the square is .

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Find the area of the pieces. \ \

Find the area of the tilted square. \ \

Side of the tilted square is .

Area of the tilted square is .

Find the area of the four triangles.

Area of the each triangle is .

Area of the four triangles is .

Sum of the areas of tilted square and four triangles is .

Area of the larger square is equal to Sum of the areas of tilted square and four triangles.

Therefore,

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Thus , the theorem is proved. \ \

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