# Pythagorean Theorem Explained The **Pythagorean The** is a fundamental principle geometry, mainly dealing with right-angled triangles. Statement For any right- triangle: - \( a \) and \( b \) be the lengths of the two sides form the right angle ( **legs**). - Let \( c \) be the length of the side opposite the right angle (called the **hypotenuse). The theorem states: \[ a^2 + b^2 = c^2 \] ## Visual Representation  *Image: Right triangle showing legs \(a\), \(b) and hypotenusec\)* ## Key Points - **Ap only to right-angled triangles.** - sum of the squares of the two shorter sides the of the longest. Example ose a right triangle has- \( a = 3 \) - \( b = 4 \Find c \): \[ c^2 =3^2 + 4^2 = 9 + 16 = 25 \im c = 5 \] ## Uses - Calculating distances (geometry, navigation,) Verifying if a triangle is right-angled - Trigonometry foundations## Why It Works The theorem proven using various methods (algebraic, geometric) and is a cornerstone of Euclidean geometry. It shows a relationship between the sides of a right triangle. --- **Summary:** The Pag The relates the side lengths of right triangle: the square of theotenuse equals sum of the squares of the other sides