Question

state and Prove the Pythagoras theorem

Answer 1

Pythagorean Theorem

The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs" (Eves 80-81).


This theorem is talking about the area of the squares that are built on each side of the right triangle. 



Accordingly, we obtain the following areas for the squares, where the green and blue squares are on the legs of the right triangle and the red square is on the hypotenuse.



area of the green square is 
area of the blue square is 
area of the red square is 



From our theorem, we have the following relationship:

area of green square + area of blue square = area of red square or

Answer 2

theorem
In a right triangle the square of hypotenuse is equal to the sum of the square of the other two sides
Proof
we are given a right triangle ABC right angled at B
we need to prove that AC^=BC^2+AB^2
let us draw BD perpendicular to AC
now,
∆ADB~∆ABC
So
AD/AB=AB/AC. (sides are proportional)
or AD.AC=AB^2........(1)
Also,∆BDC~∆ABC
So,CD/BC=BC/AC
or CD.AC°BC^2............(2)
Adding (1) and (2)AD.AC+CD.AC=AB^2+BC^2
or AC(AD+CD)=AB^2+BC^2
or AC.AC=AB^2+BC^2
AC^2=AB^2+BC^2