Theorem 5
Theorem 4
"The Corresponding Angles Theorem," also known as "The Parallel Postulate" or "The Fourth Postulate." It is a fundamental theorem in Euclidean geometry, and it states that:
"Two lines are parallel if and only if the corresponding angles formed by a transversal are congruent."
In other words, if two lines are intersected by a transversal and the corresponding angles (the angles that are on the same side of the transversal and on the same side of the lines) are congruent, then the lines are parallel. Conversely, if two lines are parallel, then their corresponding angles are congruent.
This theorem is essential in proving many other geometric properties and theorems, such as the angles formed by parallel lines and transversals, and the properties of triangles and quadrilaterals. It is often used in the study of plane geometry and has numerous applications in fields such as architecture, engineering, and physics.