In a right triangle, the square of the hypotenuse is equal to the sum

1.	In a right triangle, the square of the hypotenuse is equal to the sum of the squares of other twsides.
Answer» can show thata2+ b2= c2usingAlgebra:- 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 ofa+b, so thetotal areais: 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 thelarge squareis equal to the area of thetilted 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

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of other twsides.

Answer»

can show thata2+ b2= c2usingAlgebra:-

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 ofa+b, so thetotal areais:

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 thelarge squareis equal to the area of thetilted 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