The Pythagorean theorem states that in a right 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 can be expressed with the equation: a² + b² = c², where c represents the hypotenuse and a and b represent the other two sides of the triangle.
However, this theorem is specific to right triangles. It does not apply to other types of triangles, such as acute triangles (where all angles are less than 90 degrees) or obtuse triangles (where one angle is greater than 90 degrees). In these cases, the relationship between the sides cannot be described by the Pythagorean theorem.
For acute triangles and obtuse triangles, different formulas and principles, such as the Law of Cosines, are used to relate the lengths of the sides to the angles.
In summary, the Pythagorean theorem is a valuable tool, but its applicability is limited to right triangles only.