What Is The Pythagorean Theorem
What Is The Pythagorean Theorem
"If the triangle had a right angle that is 900 and if a square is made on each of three sides
then the biggest square has the equal area to the area if two squares put together."
This is cal ed as the "Pythagoras theorem" and Pythagorean Theorem Definition
mathematically can be written in a simple form as,
a2 + b2 = c2,
Here `c' is the longest side (the side opposite to the right angle) of the triangle and other two
that are `a' and `b' are the other sides of the triangle.
Pythagoras Theorem is a relation among three sides of a right angled triangle which states
that the area of the square whose side is opposite to the right angle is equals to the sum of the
areas of the squares of two other sides (these sides meet at the right angle).
If `c' denotes the length of the opposite side of the right angle and `a' and `b' denotes the
length of the two other sides the Pythagoras theorem is,
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a2 + b2 = c2,
If the length of the other two sides `a' and `b' are known then `c' could be calculated as,
c = (a2 + b2),
If the length of the opposite side to the right angle that is hypotenuse is `c' and one of the other
two sides either a or `b' are known then the length of the other leg can be calculated with
either of the fol owing equations,
a = (c2 - b2),
Or for the side `b'
b = (c2 - a2),
The Pythagorean equation shows the relation between sides of a triangle, thus if the lengths
of any two sides of a triangle are known then the length of the third side could be determined
easily.
In any right angle triangle the hypotenuse (that is the side that is opposite to the right angle)
here we are taking it `c', is greater than any one of the sides of the triangle but its less than the
sum of the sides of that triangle.
The formation of this theorem is basical y the law of cosines that allows the determination of
the length of the third side of the triangle and the length of the other two sides are given.
The Pythagoras theorem can be explained with the help of four copies of a right triangle that
have the sides x, y and z or it may be a, b and c. These triangles are arranged in a square of
the side `l'.
The area of a square could be presented in two different ways as,
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As the sum of the area of the two rectangles and squares,
(a + b)2 = a2 + b2 + 2ab,
As the sum of the areas of a square and the four triangles,
(a + b)2 = c2 + 4(ab / 2) = c2 + 2ab,
On putting the two right hand side equations equal,
a2 + b2 + 2ab = c2 + 2ab,
=> a2 + b2 = c2.
The converse of the Pythagoras theorem is also true according to which if a triangle satisfies
Pythagoras theorem than that triangle would be a right angle triangle.


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