Question

write all the three formula of pythagorus therom ??

Answer 1

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):

Squares and Triangles

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

Answer 2

Pythagoras Theorem Proof

Given: A right-angled triangle ABC.

To Prove- AC² = AB² + BC²

Proof: First, we have to drop a perpendicular BD onto the side AC

We know, △ADB ~ △ABC

Therefore,

AD AB

----- = -----

AB AC

(Condition for similarity)

Or, AB² = AD × AC …………………..……..(1)

Also, △BDC ~△ABC

Therefore,

CD BC

----- = -----

BC AC

(Condition for similarity)

Or, BC²= CD × AC …………………………..(2)

Adding the equations (1) and (2) we get,

AB² + BC² = AD × AC + CD × AC

AB² + BC² = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC² = AB² + BC²

Hence, the Pythagorean thoerem is proved.