Theorem of Intersection

The Theorem of Intersection states that if two geometric shapes, such as lines or circles, share some common space, then their intersection—this shared part—must also contain certain points. For example, if two lines cross, they intersect at a point; if two circles overlap, they intersect over a shared area. The theorem formalizes that the common region or points where the shapes meet always obey specific properties, allowing mathematicians to understand and predict how shapes relate when they intersect. This principle is fundamental for analyzing and solving geometric problems involving overlaps and shared regions.