The Pythagorean theorem states that, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed mathematically as:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. This theorem is fundamental in geometry and is used to determine distances, verify right angles, and solve various problems involving triangles.
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