# Pythagoras' Theorem

- Pythagoras’ Theorem is a guiding principle in geometry, specifically dealing with right-angled triangles.
- The theorem states that in a right-angle 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 lengths of the other two sides.
- This can be expressed in the formula: a² + b² = c², where ‘c’ represents the length of the hypotenuse, and ‘a’ and ‘b’ represent the lengths of the other two sides.
- This theorem only applies to right-angled triangles (triangles that include a 90-degree angle).
- To use the theorem, you must first identify the hypotenuse. In diagrams, this is typically indicated with a small square in one corner.
- Pythagoras’ theorem may be used for calculating the length of one side when the lengths of the other two sides are known.
- It can also be rearranged to find the length of either of the shorter sides.
- For example, if ‘c’ (hypotenuse) and ‘a’ are known, to find ‘b’, the formula becomes b²=c²-a². After that, b is the square root of (c²-a²).
- The theorem is highly useful in a variety of real-world applications such as construction, navigation, engineering, and graphics.
- Practice with different problems is essential to becoming familiar with using the theorem. Remember, Pythagoras’ theorem isn’t just about plugging numbers into the formula. It requires understanding of the right-angled triangle’s sides in relation to each other.
- A common mistake is to confuse which side is the hypotenuse. Always remember that it’s the side directly opposite the right angle.
- It’s also worth noting that the theorem can be used as a test to check if a triangle is right-angled. If a² + b² = c², then the triangle must be a right triangle.
- So, when revising Pythagoras’ Theorem, remember: identify the hypotenuse, square the lengths, add or subtract, and square root the answer if necessary. And above all, practise!