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Consider a square with a slightly smaller square just inside, the smaller square being rotated so that the corners just touch the sides of the larger square. The four spaces between the two squares are four exactly equal right angled triangles. If we call the sides of these triangles h=hypotenuse, L=long side and s=short side then we see that the area of the small square is h squared and the area of the large square is (s +L) squared =s squared + L squared +2s x L. The area of the four triangle is (4 x s x L)/2
By simple arithmetic:- the area of the small square (h squared) = The area of the large square minus the area of the four triangles, h squared = s squared +L squared + 2s x L - (4/2 x s x L). The last two terms cancel each other out leaving h squared = s squared + L squared.
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What type of triangle is used in Pythagoras theorem?
Right triangle ( triangle in which one angle is 90 degrees)
Pythagoras is often described as what?
"The father of numbers."Pythagoras was an ancient Greek mathematician famous for his theorem for a right angle triangle.
Why does Pythagoras theorem work?
Pythagoras' theorem states that for any right angle triangle the square of its hypotenuse is equal to the sum of its square sides
Does the theorem hold true if the triangle is not a right triangle?
Pythagoras' theorem is only applicable to a right angle triangle in that the square of its hypotenuse is equal to the sum of its two squared sides.
Is a triangle with sides of lengths 20 21 and 29 a right triangl?
Yes because the given dimensions comply with Pythagoras's theorem for a right angle triangle.
