A look into the proof of Pythagorean theorem

As we know already, the Pythagorean theorem denotes that the squares of two sides of a right angle triangle equal to the length of its third side. To put it simply for those who are interested in acquiring proof of Pythagorean theorem, it can be denoted as:

A² + B² = C²

A basic and simple Pythagorean theorem proof

Here is a very simple Pythagorean theorem proof. For it, we basically start off with two squared that have the sides a and b, both of which are placed side by side. For this square, the sum of the area of the two squared would be a² + b². The square would be something like this:

pythahorean_theorem_proof_a_b

Now, within the square, draw two triangles that have a hypotenuse c and sides and b. Once the triangles are attained, we just rotate the triangles at a 90 degree angle, both of them around their very own top vertex.

pythahorean_theorem_proof_a_b_ñ

Remember that the triangle on the right is to be rotated clockwise, whether the one of the left is to be rotated counter-clockwise. On the whole, this is going to formulate a square with a side c, wherein its area is to be c².

pythahorean_theorem_proof_a_b_c2

A look into Euclid proof for Pythagorean theorem

The Euclid proof is basically based over two propositions which states that similar polygons can be divided into similar triangles. These triangles are equal in terms of multitude and as a whole their ratios are the same too. Moreover, ratio that the polygon has to a polygon is the same as that which is common amid corresponding sides. Also, the ratio that similar triangles have to each other is the same as that of their corresponding sides. When you go into the details of the Euclid proof, you would find that it provides ample geometric proof of Pythagorean Theorem.

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