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Given its long history, there are numerous proofs (more than 350) of the Pythagorean theorem, perhaps more than any other theorem of mathematics. The proofs below are by no means exhaustive, and have been grouped primarily by the approaches used in the proofs.
The Pythagorean theorem says that, in a right triangle, the square of a (which is a×a, and is written a2) plus the square of b (b2) is equal to the square of c (c2): a 2 + b 2 = c 2. Proof of the Pythagorean Theorem using Algebra. We can show that a2 + b2 = c2 using Algebra.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
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The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c 2 = a 2 + b 2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
5 ημέρες πριν · The various proofs of the Pythagorean theorem all seem to require application of some version or consequence of the parallel postulate: proofs by dissection rely on the complementarity of the acute angles of the right triangle, proofs by shearing rely on explicit constructions of parallelograms, proofs by similarity require the existence of non ...
In the figure, the triangles whose are areas are marked x and y are similar to the original triangle (which has area x+y). So accepting that areas of similar right-angled triangles are proportional to the squares of the hypotenuse, x:y:x+y are in ratio a 2:b 2:c 2, which is Pythagoras's theorem.
The Pythagorean theorem gives us the relation between the three sides of a right triangle. It is named after Pythagoras, the great Greek polymath (although the theorem was known to different civilizations for centuries before Pythagoras).
