Theorem of Pythagoras
Apply Pythagoras in right-angled triangles
The Theorem of Pythagoras
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle).
Example
Finding the Hypotenuse
A right triangle with sides 3 cm and 4 cm:
c² = 3² + 4² = 9 + 16 = 25
c = √25 = 5 cm
Sides 5 m and 12 m:
c² = 25 + 144 = 169
c = √169 = 13 m
Example
Finding a Shorter Side
Hypotenuse = 10 cm, one side = 6 cm:
a² + 6² = 10²
a² + 36 = 100
a² = 64
a = √64 = 8 cm
Note
Remember
The theorem ONLY works for right-angled triangles. The hypotenuse is always the longest side and is opposite the 90° angle. Check: if a² + b² = c², the triangle is right-angled.
Key Vocabulary
HypotenuseThe longest side of a right triangle (opposite the right angle)
Right angleAn angle of exactly 90°
TheoremA mathematical statement that has been proved true
Square rootThe number that multiplied by itself gives the original (√)
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Hypotenuse
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