Here is a detailed explanation of Pythagoras Theorem. This theorem is applicable to Right Angle Triangles only. Hope you will get a better understanding through this presentation. Thank You.. Regards Mukul Garg

1. PYTHAGORAS THEOREM
(PROOF OF PYTHAGORAS THEOREM)

2. STATEMENT :- According to the Pythagoras theorem
“In a Right angled Triangle, the square of the hypotenuse
is equal to the sum of individual squares of the other two
sides”.
i.e (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

3. Right Angled Triangle
hypotneuse
base
perpendicular
A
B C
Acc. To Pythgoras Theorem
(Hypotneuse)^2 = (Base)^2 + (Perpendicular)^2
(AC)^2 = (AB)^2 + (BC)^2

4. Proof of Pythagoras Theorem
A
B C
D
x
90 - x
90
90
ABC is a right angled triangle .Draw a perpendicular BD on AC.
Now , there are two more right angle triangle i.e, tri.(BCD) and tri.(BAD)
Therefore, AC = AD + CD
In tri.(BCD),
Cos x = base
hypotneuse
Cos x = CD
BC
So, CD= BC Cosx--eq1
In tri.(BAD),
Cos (90 - x) = base
hypotneuse
Cos (90 - x) = AD
AB
So, AD = AB Sinx --eq2 (cos(90-x) = sinx)
Also, in tri(ABC),
Sin x = perpendicular
hypotneuse
Sinx = AB
AC
Cos x = base
hypotneuse
Cos x = BC
AC

5. Since, AC = AD + CD
By putting value of AD and CD from eq1 and eq2
We have, AC = AB Sin x + BC Cos x
Now, putting Sin x = AB and Cos x = BC in above equation,
AC AC
We have, AC = AB( AB ) + BC( BC )
( AC ) ( AC)
AC x AC = (AB)^2 + (BC)^2
(AC)^2 = (AB)^2 + (BC)^2

6. THANK YOU