1. The problem is to understand and apply the Pythagorean theorem, which relates the lengths of the sides of a right triangle. 2. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two sides ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. Important rules: - The triangle must be right-angled. - $c$ is always the side opposite the right angle (the longest side). 4. To find the length of one side, rearrange the formula. For example, to find $a$: $$a = \sqrt{c^2 - b^2}$$ 5. Example: If $a=3$ and $b=4$, find $c$. $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ $$c = \sqrt{25} = 5$$ 6. This means the hypotenuse is 5 units long. This theorem helps solve many geometry problems involving right triangles.