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Middle school📐Geometry●●○○○· 5 min
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Pythagoras' theorem, without formulas: the 3-squares proof

A right triangle, three squares drawn on its sides. The visual trick that makes the formula obvious.

The theorem in 5 words

The big square equals the two small ones.

See for yourself:

Pythagoras in 3 steps

Étape 1 / ?

CBAa = 3b = 4c = ?
Step 1 — A simple right triangle (3, 4, 5).
a²b²c²
Step 2 — Draw a square on each side.
916259 + 16 = 25 ✓
Step 3 — Area(green) + Area(orange) = Area(red). That's Pythagoras!

In formula

For a right triangle with sides a, b (the two shorter ones) and c (the hypotenuse, opposite the right angle):

a2+b2=c2a^2 + b^2 = c^2

Real-world uses

Need the length of a leaning ladder, the diagonal of a screen, the distance between two points on a map… Pythagoras answers all of these. Just remember: square + square = square.

?Your turn

A right triangle has sides 5 cm and 12 cm, plus a hypotenuse. How long is the hypotenuse?

#pythagoras#triangle#square#proof

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