Pythagoras proof. An easy to understand proof of Pythagoras Theorem a^2 + b^2 = c^2
In this hub I will show you a simple proof of Pythagoras Theorem, that is, the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides:
a² + b² = c².
The proof can be done by fitting 4 congruent right angled triangles together to make a square and writing the area of the square down in 2 different ways. This is probably one of the easier and nicer proofs of Pythagoras.
First start off with a right angled triangle and call the sides a,b and c (c being the hypotenuse).
Next you will need to draw another 3 congruent triangles to this first right angled triangle by rotating it through 90⁰, 180⁰ and 270⁰ clockwise.
Fit these 4 triangles together to make a square of side length a + b. You will also notice that there is a square of side length c made inside the larger square.
Now the area of the large square has an area of (a+b)(a+b). If you expand and simplify these double brackets you get A = a² + 2ab + b². Call this formula 1.
You can also make another formula for the area of the large square by summing the area of the four triangles and the smaller square inside the large square:
4 × ½ × a × b + c × c
So A = 2ab + c²
Call this formula 2.
So the two formulas that we have made for the area of the large square are:
A = a² + 2ab + b² and A = 2ab + c².
All you need to do is equate both formulas as both formulas made give the area of the large square:
a² + 2ab + b² = 2ab + c².
If you notice there is a 2ab term on both sides of the equation. All you need to do now is subtract 2ab from both sides. This will give you the required result:
a² + b² = c²
More by this Author
To calculate the 3 point moving averages form a list of numbers, follow these steps: 1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving...
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...
No comments yet.