Pythagorean Theorem

What is the Pythagorean theorem?

It is a rule about right triangles. A right triangle has one corner that makes a perfect L, like the corner of a book.

The two short sides are called the legs. The long side across from the L is called the hypotenuse. The rule says that if you square each leg and add them, you get the square of the hypotenuse.

You might remember it written as a² + b² = c². Here a and b are the legs and c is the hypotenuse.

What is this module?

The module draws a right triangle with a slider for each leg. Move a slider and the triangle changes shape.

It also draws a square on every side. The two smaller squares together hold the same area as the largest square. That is what the rule means.

What they're learning

The legs and the hypotenuse are linked. Change a leg and the hypotenuse changes too.

• The names of the parts of a right triangle: legs and hypotenuse.
• How to use the rule a² + b² = c².
• That the largest square always sits on the longest side.
• That doubling both legs doubles the hypotenuse.

Aliases

• Pythagoras
• a² + b² = c²
• Right triangle rule
• 3-4-5 triangle

Refresher

In a right triangle, square the two short sides, add them, and you get the square of the long side. The long side is the hypotenuse, and it sits across from the square corner.

Try this together

You don't have to teach a whole lesson. A few minutes with the sliders is enough.

1. Set leg a to 120 and leg b to 90. Ask your kid what the long side will be before checking.
2. Look at the readout together. It shows 150.
3. Set both legs to 40. Ask whether the hypotenuse will be more or less than 80. It comes out less, about 57.
4. Point at the squares. Ask which one is biggest and why.

If you're stuck, change one slider at a time and watch what happens to the squares.

Words you might hear

• Right triangle: a triangle with one square corner.
• Leg: one of the two shorter sides, next to the square corner.
• Hypotenuse: the longest side, across from the square corner.
• Squared: a number multiplied by itself. 5 squared is 25.

Deeper dive

Try legs of 3 and 4. Square each one: 9 + 16 = 25. The hypotenuse is the number that squares to 25, which is 5.

The module draws a square on each side, and you can see the two smaller squares together hold the same area as the big one. Double both legs and the hypotenuse doubles too. A leg of 3 and a leg of 4 always give a hypotenuse of 5.