Pythagoras' theorem

In a right-angled triangle, the square on the longest side (the hypotenuse) has the same area as the squares on the two shorter sides together: for sides of 3, 4 and 5, 9 + 16 = 25. So two sides give you the third, and a triangle whose sides fit the rule always has a right angle.

Depth 1 · Foundation

You can see that the squares on the two shorter sides of a right-angled triangle make the square on the longest side, find the longest side from the other two with a square root, and check a right angle with 3, 4 and 5.

Depths of understanding

1
Foundation
You can see that the squares on the two shorter sides of a right-angled triangle make the square on the longest side, find the longest side from the other two with a square root, and check a right angle with 3, 4 and 5.
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- Squares on a Right TriangleGeometry Level 1: Shapes and Space
Opens after
TrianglesPythagoras' theorem is about right-angled triangles and their longest side.Area, depth 2The theorem compares the areas of squares, and the area of a square is its side times itself.Square numbersThe squares on the sides of a 3, 4, 5 triangle are the square numbers 9, 16 and 25.Square rootsTo get a side back from the area of its square you take a square root: √25 = 5.

Your path here

What's still between you and Pythagoras' theorem, depth 1, in the order you can learn it.

Where it fits

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Triangles AreaDepth 2 Square numbersNumber Theory Square rootsArithmetic

This concept

Pythagoras' theoremGeometry

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Irrational numbersNumber Systems

Builds onThis conceptOpens upTriangles AreaDepth 2 Square numbersNumber Theory Square rootsArithmetic Pythagoras' theoremGeometry Irrational numbersNumber Systems