explain pgt theorem with fig.
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The Pythagorean Theorem says that, in a right triangle, the square of a (a2) plus the square of b (b2) is equal to the square of c (c2):
a2 + b2 = c2
Proof of the Pythagorean Theorem using Algebra
We can show that a2 + b2 = c2 using Algebra
Take a look at this diagram ... it has that "abc" triangle in it (four of them actually):

Area of Whole Square
It is a big square, with each side having a length of a+b, so the total area is:
A = (a+b)(a+b)
Area of The Pieces
Now let's add up the areas of all the smaller pieces:
First, the smaller (tilted) square has an area of:c2
Each of the four triangles has an area of:ab2
So all four of them together is:4ab2 = 2ab
Adding up the tilted square and the 4 triangles gives:A = c2 + 2ab
Both Areas Must Be Equal
The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:
(a+b)(a+b) = c2 + 2ab
NOW, let us rearrange this to see if we can get the pythagoras theorem:
Start with:(a+b)(a+b) = c2 + 2ab
Expand (a+b)(a+b):a2 + 2ab + b2 = c2 + 2ab
Subtract "2ab" from both sides:a2 + b2 = c2
I Hope this is helpful for u......
a2 + b2 = c2
Proof of the Pythagorean Theorem using Algebra
We can show that a2 + b2 = c2 using Algebra
Take a look at this diagram ... it has that "abc" triangle in it (four of them actually):

Area of Whole Square
It is a big square, with each side having a length of a+b, so the total area is:
A = (a+b)(a+b)
Area of The Pieces
Now let's add up the areas of all the smaller pieces:
First, the smaller (tilted) square has an area of:c2
Each of the four triangles has an area of:ab2
So all four of them together is:4ab2 = 2ab
Adding up the tilted square and the 4 triangles gives:A = c2 + 2ab
Both Areas Must Be Equal
The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:
(a+b)(a+b) = c2 + 2ab
NOW, let us rearrange this to see if we can get the pythagoras theorem:
Start with:(a+b)(a+b) = c2 + 2ab
Expand (a+b)(a+b):a2 + 2ab + b2 = c2 + 2ab
Subtract "2ab" from both sides:a2 + b2 = c2
I Hope this is helpful for u......
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