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Pythagoras Theorem
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Pythagoras theorem   
In a right angled triangle the square of the longest side is equal to the sum of the squares of the other two sides.
The longest side of the triangle is called the "hypotenuse".
In algebraic terms, we can write a2 + b2 = c2, where c is the hypotenuse while a and b are two other sides of the triangle.
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Example: In Fig.,ABC is a right triangle, right angled at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and AD = (35)/2 cm, find the length of CE.
Solution: Since ABD is a right triangle, right angled at B. Therefore,
AD2 = AB2 + BD2
AD2 = AB2 + (BC/2)2
AD2 = AB2 + (1/4)BC2........(i)
Again, BCE is right triangle, right angled at B
CE2 = BC2 + BE2
CE2 = BC2 + (AB/2)2
CE2 = BC2 + (1/4)AB2.........(ii)
adding Equations (i) and (ii) you get
AD2 + CE2 = AB2 + 1/4BC2 + BC2 + 1/4AB2
AD2 + CE2 = 5/4(AB2 + BC2)
AD2 + CE2 = 5/4(AC2)  [ ABC is right triangle AC2 = AB2 + BC2 ]
(35/2)2 + CE2 = 5/4 * 25
CE2 = 125/4 - 45/4
CE = 20 cm= 25 cm
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