This theory is the fundamental principal of Trinogemetry! It's named after the great Greek mathematician Pythagoras.
The Theorom says, In a right angled ∆ABC, right angled at A,
There are two proofs for it.
Take for identical right angled traingle where side length is a and b and hypotonuse is c
Arrange them like thier hypotonuse form a square (as shown in fig.1) Now, area of the square formed is c²
Now, rearrange the traingles into two rectangles (as shown in Fig.2) Areas of both squares are now a² and b²
The areas of both squares (fig.1 and fig.2) are same. So, empty space must be equal.
So, c² = a² + b² Hence, Proved!
This proof is based on the property, 'If a right angle divides the traingle into 2, and if the corresponding angles of the two traingles are same, then the ratios of three sides is same.
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Proof of Pythagorean Theorom!
This theory is the fundamental principal of Trinogemetry! It's named after the great Greek mathematician Pythagoras.
The Theorom says, In a right angled ∆ABC, right angled at A,
There are two proofs for it.
Take for identical right angled traingle where side length is a and b and hypotonuse is c
Arrange them like thier hypotonuse form a square (as shown in fig.1) Now, area of the square formed is c²
Now, rearrange the traingles into two rectangles (as shown in Fig.2) Areas of both squares are now a² and b²
The areas of both squares (fig.1 and fig.2) are same. So, empty space must be equal.
So, c² = a² + b²
Hence, Proved!
This proof is based on the property, 'If a right angle divides the traingle into 2, and if the corresponding angles of the two traingles are same, then the ratios of three sides is same.
For 3 Similar traingles, (as given in Fig.3)
and
(Refer Fig 4)
AC² = BC × CD
AB² = BC × BD
AB² + AC² = BC (CD + BD)
AB² + AC² = BC²
A² + B² = C²
Hence, Proved.
Pardon me for the figures/ drawings ^^
Glad if helped :)