The Pythagorean theorem is a fundamental principle in geometry that relates to right triangles. It states that in a right triangle (a triangle with one angle measuring 90 degrees), 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.
The theorem is usually expressed with the formula:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.
This theorem is significant for various reasons:
- It provides a method for calculating the lengths of sides in right triangles.
- It serves as the foundation for various aspects of trigonometry and algebra.
- It has practical applications in fields such as construction, navigation, computer graphics, and physics.
The Pythagorean theorem only applies to right triangles, making it one of the essential tools for understanding the properties and relationships within triangle geometries.
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