Long before anyone wrote down a theorem about right-angled triangles, builders needed right angles, and they had a tool for making them that cost nothing: a loop of rope with twelve knots tied at equal intervals.
Three people take hold of the loop, one at the first knot, one at the fourth, one at the eighth, and pull it tight. The rope forms a triangle with sides of three, four and five spaces, and the angle between the short two is exactly a right angle. Every time. Nobody has to measure anything.
It works because three multiplied by itself, plus four multiplied by itself, comes to exactly the same number as five multiplied by itself. That is not a rough agreement, and the corner is not nearly square. It is square.
The usefulness of the trick is that it travels. It needs no instrument, no degrees, and no writing. A rope and three pairs of hands will lay out the corner of a foundation in a field with nothing else available, and the corner will be true.
The rope is a theorem you can hold. Nothing about it needs to be believed on trust: pull it tight and the corner is there.
Modern builders still use it, usually with a tape measure instead of knots and often with larger numbers — six, eight and ten, or nine, twelve and fifteen. The numbers change and the reason does not: any three lengths in that proportion close into a right angle.