Geometry is the mathematical study of shapes, sizes, positions, and spatial relationships in two and three dimensions. It forms the foundation for understanding our physical world — from architecture and engineering to computer graphics and navigation. At its core, geometry involves points, lines, angles, and figures that combine to create everything from simple triangles to complex polyhedra. The field divides into plane geometry (2D shapes on flat surfaces), solid geometry (3D objects in space), and analytic geometry (coordinates and algebraic methods). A key mental model: every geometric relationship can be proven using logic — unlike arithmetic where you calculate, in geometry you construct, measure, and demonstrate why things must be true.
What This Cheat Sheet Covers
This topic spans 29 focused tables and 238 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
Table 1: Basic Elements
| Element | Example | Description |
|---|---|---|
A, B, P | • Exact location in space with no size or dimension • named with capital letters. | |
\overleftrightarrow{AB} | Infinite straight path extending in both directions with no endpoints. | |
\overline{AB} | Portion of a line with two endpoints and measurable length. | |
\overrightarrow{AB} | Part of a line with one endpoint extending infinitely in one direction. | |
Plane ABC | Flat, two-dimensional surface extending infinitely in all directions. | |
AB \parallel CD | • Lines in the same plane that never intersect • always equidistant. |