Lay three pairs of shoes on the floor in a right triangle. Measure each side. Check if a² + b² = c².
Make the triangle right first
The check a² + b² = c² only works when the angle between sides a and b is exactly 90°. Drag a corner above until 'right' shows — then the square on the longest side equals the sum of the squares on the other two, every time.
Two shoes are 9 cm and 12 cm apart along the legs of a right angle. How far apart are the far ends (the hypotenuse)?
Reverse it: if you measure three lengths and 3² + 4² = 5² holds, the triangle must be right-angled. Builders use a 3-4-5 string loop to lay out square corners with no protractor.
Sides 30 cm, 40 cm. Hypotenuse?
30² + 40² = 900 + 1600 = 2500. √2500 = 50 cm. So the hypotenuse should measure 50 cm.
There are over 350 known proofs of Pythagoras' theorem — including one by US President James Garfield.