MISSION · Geometry
The Pythagorean Theorem
Connect the sides of a right triangle with one powerful rule
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
In a right triangle, the square of the longest side equals the sum of the squares of the other two sides.
Know which side is c
The formula is:
\[a^2 + b^2 = c^2\]The side \(c\) is always the hypotenuse: the longest side, across from the right angle. The two shorter sides can be \(a\) and \(b\) in either order.
Find a missing hypotenuse
If the shorter sides are 6 and 8:
\(6^2 + 8^2 = c^2\) \(36 + 64 = c^2\) \(100 = c^2\) \(10 = c\)
The hypotenuse is 10 units long.
Find a missing shorter side
If the hypotenuse is 13 and one shorter side is 5:
\(a^2 + 5^2 = 13^2\) \(a^2 + 25 = 169\) \(a^2 = 144\) \(a = 12\)
Side lengths are distances, so use the positive square root.
Common mix-ups
- Using the formula on a triangle without a right angle.
- Calling the unknown side \(c\) automatically. Only the hypotenuse is \(c\).
- Forgetting the square root at the end. If \(c^2 = 100\), then \(c = 10\), not 100.
Check yourself
A right triangle has shorter sides 9 and 12. Find the hypotenuse.
\(9^2 + 12^2 = 81 + 144 = 225\), and \(\sqrt{225} = 15\).
LEVEL 3 · REFLECT
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