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Pythagorean theorem

Pythagorean theorem

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Pythagorean Theorem, its proofs and applications

Let us consider a triangle with one of the angles being right angled shown below in figure 1:

Figure 1

Such a triangle has a very special relationship between its sides in geometry. This relation was first

discovered by the Greek Mathematician-Philosopher Pythagoras, which is basically why it is named

after him.

The theorem states that the square of the side that is the hypotenuse (the side opposite to right

angle) is the sum of the other two sides. If we let the hypotenuse to be c and the other two sides to

be a and b we can represent this mathematically by;

c

2

= a

2

+ b

2

Proof:

Consider a the following square (exterior) is made up of 4 right-angled triangles below.

We can see that each side has length c which is the hypotenuse while each side of interior square

has length b – a.

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Pythagorean Theorem, its proofs and applications Let us consider a triangle with one of the angles being right angled shown below in figure 1: Figure 1 Such a triangle has a very special relationship between its sides in geometry. This relation was first discovered by the Greek Mathematician-Philosopher Pythagoras, which is basically why it is named after him. The theorem states that the square of the side that is the hypotenuse (the side opposite to right angle) is the sum of the other two sides. If we let the hypotenuse to be c and the other two sides to be a and b we can represent this mat ...
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