Prove pythagoreas theorm

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Gaurav Seth 6 years, 1 month ago
Pythagoras Theorem
Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
Given: A right triangle ABC right angled at B.
To prove: AC2 = AB2 + BC2
Construction: Draw BD
AC
Proof :
We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.
So,
(Sides are proportional)
Or, AD.AC = AB2 ... (1)
Also,
BDC 
ABC
So,
Or, CD. AC = BC2 ... (2)
Adding (1) and (2),
AD. AC + CD. AC = AB2 + BC2
AC (AD + CD) = AB2 + BC2
AC.AC = AB2 + BC2
AC2 = AB2 + BC2
Hence Proved.
1Thank You