Explain a proof of the Pythagorean theorem In 5 sentences
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. To prove this, we start by drawing a right-angled triangle with sides of length 'a' and 'b' and hypotenuse of length 'c'. We then construct a square with side length 'a+b' and divide it into four smaller squares. By rearranging these smaller squares, we can form a smaller square with side length 'c' and prove that its area is equal to the sum of the areas of the squares with side lengths 'a' and 'b'. Since the area of a square is equal to the square of its side length, the equation holds true: c^2 = a^2 + b^2, which is the Pythagorean theorem.
1. To prove the Pythagorean theorem, start with a right-angled triangle with side lengths 'a', 'b', and 'c', where 'c' is the hypotenuse.
2. Now, draw a square on each side of the triangle. The area of the square formed on the hypotenuse would be equal to the sum of the areas of the squares formed on the other two sides.
3. The square on side 'a' would have an area of 'a^2', and the square on side 'b' would have an area of 'b^2'.
4. The area of the square formed on the hypotenuse, 'c^2', would then be equal to 'a^2 + b^2'.
5. Thus, the Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, or mathematically, c^2 = a^2 + b^2.