Pythagoras Theorem Working Model

A puzzle proof of Pythagoras theorem. The yellow square fills the square on side a, the four red triangles fill the square on side b, and all five pieces together fill the square on the hypotenuse exactly.

How it works

1. Place the yellow square in the small square on side a (5 cm)
2. Fit the four red triangles into the square on side b (10 cm)
3. Move all five pieces into the square on the hypotenuse. They fill it with no gaps, so a² + b² = c²

What students learn

• The square on the hypotenuse has the same area as the squares on the other two sides put together
• The hypotenuse is the side opposite the right angle and is always the longest side
• With a = 5 cm and b = 10 cm, c² = 25 + 100 = 125, so c is about 11.2 cm

Try these activities

1. Measure the hypotenuse of the tray and check that c² comes close to 125
2. Let groups race to move the pieces from the two small squares into the big one
3. Use the theorem to test whether triangles with sides 3, 4, 5 and 6, 8, 10 are right-angled

Curriculum fit

In the box

• MDF tray with a right triangle of sides a = 5 cm and b = 10 cm
• 4 red acrylic triangles and 1 yellow acrylic square
• Step-by-step manual

Pairs well with

Pythagoras Theorem Kit (Senior)MATH-124Two Congruent Right TrianglesMATH-122