Pythagoras' theorem
Pythagoras sats
MathRare
Discovered 1800 BC · Babylon
SPARKON01 / 10
Pythagoras' theorem
The ideaIn a right-angled triangle, the squares on the two short sides add up to the square on the long side.
a² + b² = c²
Lets you predictA distance you cannot measure, from two you can.
Tests usually ask
- Find the missing side
- Is this triangle right-angled?
Scan for the full explanation and a practice question.
SPARKON · 01 / 10
SPARKON · 01 / 10
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Math ◆ Rare: a famous discovery
Pythagoras' theorem
In a right-angled triangle, the squares on the two short sides add up to the square on the long side.
a² + b² = c²
Why it works
Draw a square on each side of a right-angled triangle. The two small squares together always cover exactly the same area as the big one. That is the whole theorem.
Clay tablets from Babylon list triangles like 3, 4, 5 more than a thousand years before Pythagoras was born. Builders used a rope with 12 equal knots to make a perfect right angle: 3 + 4 + 5 knots.
What it lets you predict
A distance you cannot measure, from two you can.
How tests ask about it
- Find the missing side
- Is this triangle right-angled?
Try it
A phone screen is 6 cm wide and 8 cm tall. How long is the diagonal?
Show the answer
6² + 8² = 36 + 64 = 100, so the diagonal is √100 = 10 cm.
Connects to
Wins these Lab Duel challenges
- Will a 5 m ladder reach a window 4 m up if its foot must stand 3 m out? see challenge