The theorem itself is rock-solid. The slips happen when we mislabel the hypotenuse, or reach for the rule on a triangle that was never entitled to it.
Trap One: the Hypotenuse Isn't "the Bottom"
Because textbooks usually draw the slanted long side along the base, people start believing the hypotenuse is wherever the bottom is. It isn't. Spin the triangle in the toy and the longest side ends up on top, on the side, anywhere — but it's always the one sitting straight across from the right angle. The right angle points at its hypotenuse like an arrow.
Trap Two: Only Right-angled Triangles Allowed
Pythagoras' theorem is a deal that comes with one strict condition: there must be a right angle. Bend the apex in the toy so the marked angle is, say, 70° or 100°, and the equation falls apart — a² + b² no longer matches c². The little square marker is your permission slip. No square corner, no theorem.
How to Stay Safe
Two quick checks before you ever write a² + b² = c². First, is there a right angle? Look for the box, or for wording that promises one. Second, which side is opposite it? That side, and only that side, is your c. Do those two checks and both traps simply vanish.