Geometric theorems are statements in geometry that have been proven to be true based on previously established facts, definitions, and axioms. They help us understand the properties and relationships of shapes, angles, and lines. Famous examples include the Pythagorean Theorem, which relates the sides of a right triangle, and Euclid's postulates, which form the foundation of classical geometry. These theorems are essential for solving geometric problems and are widely used in various fields, including architecture, engineering, and computer graphics. By applying geometric theorems, we can make accurate predictions about spatial relationships and design effective solutions in real-world applications.