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Identifying Pythagoras' Theorem
Rung 2 of 4 · The method

Naming the Parts, Stating the Theorem

Before you can use Pythagoras you have to read a triangle properly — spot the hypotenuse, see the two legs, and write the rule the right way round.


PractiseA new right triangle each time, tilted every which way. Tap the side you reckon is the hypotenuse.
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Every right-angled triangle has the same three named parts. Learn to point at them instantly and the theorem more or less writes itself.

The Three Parts

The right angle — the square corner, usually shown with a little box. The hypotenuse — the longest side, and it always sits directly opposite the right angle. The two legs — the other two sides, the ones that meet to make the right angle. We label the legs a and b, and the hypotenuse c.

State the Theorem

With the parts named, the rule is just one line: a² + b² = c². In words: the square of the hypotenuse equals the sum of the squares of the other two sides. The hypotenuse has to be the c — the lone term on its own side of the equals sign — because it's the biggest square.

Say it plainly: hypotenuse = longest side, opposite the right angle, call it c. The two legs are a and b. The rule: a² + b² = c².

A Worked One — Just Reading It

Picture a right triangle with legs of 6 and 8 and a slanted side of 10. Which is the hypotenuse? The 10 — it's the longest and it faces the square corner. So a = 6, b = 8, c = 10, and the theorem reads 6² + 8² = 10², i.e. 36 + 64 = 100. Notice we haven't solved for anything — we've just identified the parts and written the rule correctly. That's the whole job on this rung.

Why Getting C Right Matters

Put the wrong side as c and the equation is simply false. The hypotenuse earns its lonely spot because its square is the big one the other two add up to. Naming first, formula second — never the other way round.

Us, Thinking Out Loud

Could you point to the hypotenuse on a triangle tipped on its side?

Why must the hypotenuse always be the longest side?