Pythagorean Theorem
What the Theorem Says
In a right‑angled triangle the longest side (the Hypotenuse) is special.
If the two shorter sides are called A and B, then
[ a^2 + b^2 = c^2 ]
where C is the length of the hypotenuse. In words: the square of the hypotenuse equals the sum of the squares of the other two sides.
How to Use It
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Find the right angle in the triangle.
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Give the short sides the letters A and B, and the long side C.
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Square the numbers for A and B (multiply each by itself).
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Add those two results together.
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If you need C, take the square root of the sum (the number that, when multiplied by itself, gives the sum).
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If you are missing A or B, rearrange the formula:
a² = c² – b² or b² = c² – a²
then take the square root.
A Simple Example
Suppose a triangle has sides 3 cm and 4 cm, and we want the hypotenuse.
- 3² = 9
- 4² = 16
- 9 + 16 = 25
- √25 = 5
So the hypotenuse is 5 Cm long.
Why It Matters
The Pythagorean theorem helps us find distances we can’t measure directly.
- Builders use it to check that walls are square.
- Engineers design safe ramps and bridges.
- Gamers calculate straight‑line paths in video games.
Whenever you need to know the shortest distance between two points on a flat surface, the theorem is a handy tool.