3. The Pythagorean Theorem

The central formula for right triangles is the Pythagorean Theorem:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse.

The theorem says that the squares on the two legs add up to the square on the hypotenuse. For a 3-4-5 triangle:
\[ 3^2 + 4^2 = 9 + 16 = 25 = 5^2. \]

Use this theorem when a question asks for a missing side, a diagonal, a straight-line distance, a ladder height, or a ramp length.

Common mistake: writing \(a + b = c\). Side lengths do not add directly; their squares do.