The Pythagorean Theorem is a fundamental principle in geometry that applies to right-angled triangles. It states:

$a^2 + b^2 = c^2$

Where:

• $a$ and $b$ are the lengths of the two legs of the right triangle (the sides forming the right angle).
• $c$ is the length of the hypotenuse (the side opposite the right angle).

Example:

If one leg of a triangle is 3 units, the other leg is 4 units, then the hypotenuse can be found using the theorem:

$3^2 + 4^2 = c^2$ $9 + 16 = c^2$ $25 = c^2 \quad \Rightarrow \quad c = \sqrt{25} = 5$

So, the hypotenuse is 5 units.

Would you like more details or have any questions?

Here are five related questions:

1. How do you apply the Pythagorean Theorem to find the length of one leg if the hypotenuse and the other leg are known?
2. Can the Pythagorean Theorem be used in non-Euclidean geometry?
3. How is the Pythagorean Theorem used in three-dimensional space?
4. What are Pythagorean triples and how are they derived?
5. Can the Pythagorean Theorem help in calculating distances on a coordinate plane?

Tip: The Pythagorean Theorem only applies to right triangles, so check that there's a 90° angle first!