The Right-Angle Rule

In any right triangle, the square of the hypotenuse (the longest side, opposite the 90° corner) equals the squares of the other two sides added together: a² + b² = c².

Try it. If the short sides are 3 and 4, then c = √(9 + 16) = √25 = 5. That single relationship is the most useful fact in all of geometry, and you're about to see why.

The rule has one condition: the triangle must have a 90° angle. No right angle, no formula.

That sounds limiting until you look around. Walls meet floors, screens have square corners, streets cross, ladders lean against walls. Wherever two measurements sit at right angles and you need the slanted distance between their ends, Pythagoras hands you the answer.