Solution:** For a right triangle, the Pythagorean theorem states:

Sun, 03 May 2026 05:15:15 +0000

# Understanding the Pythagorean Theorem: The Solution for Right Triangles When studying geometry, one of the most foundational and powerful tools for working with right triangles is the Pythagorean Theorem. This timeless mathematical principle not only helps solve for unknown side lengths but also deepens our understanding of spatial relationships. Whether you're learning algebra, engineering, architecture, or even applied sciences, mastering this concept is essential. In this SEO-optimized article, we explore the Pythagorean Theorem — its definition, proof, applications, and why it remains a cornerstone of mathematical problem-solving. ## What Is the Pythagorean Theorem? The Pythagorean Theorem expresses a fundamental relationship in right triangles — triangles with one 90-degree angle. According to the theorem, the square of the hypotenuse (the longest side opposite the right angle) is equal to the sum of the squares of the other two sides, called the legs. Formally stated: In any right triangle, if a and b are the lengths of the legs, and c is the hypotenuse, then: $$ a^2 + b^2 = c^2 $$