An overview of basic geometry concepts, including points, lines, angles, polygons, and geometric shapes.
Introduction to Geometry – Study Notes
| Concept | Description | Typical Notation |
|---|---|---|
| Point | Location with no size or dimension. | (A, B, P) |
| Line | Extends infinitely in two directions; one‑dimensional. | ( \overleftrightarrow{AB}) |
| Ray | Starts at a point and extends infinitely in one direction. | ( \overrightarrow{AB}) |
| Segment | Part of a line bounded by two endpoints. | (\overline{AB}) |
| Plane | Flat, two‑dimensional surface extending infinitely. | ( \Pi) |
| Angle | Measure of rotation between two rays sharing a vertex. | (\angle ABC) |
| Polygon | Closed figure formed by straight line segments. | Triangle, quadrilateral, etc. |
| Solid | Three‑dimensional object (e.g., cube, sphere). | — |
| Branch | Focus | Example Topics |
|---|---|---|
| Euclidean | Flat space; based on Euclid’s postulates. | Parallel lines, triangle congruence. |
| Non‑Euclidean | Curved spaces (hyperbolic, spherical). | Spherical triangles, hyperbolic tilings. |
| Analytic | Uses coordinates & algebra to study geometric objects. | Distance formula, equations of circles. |
| Transformational | Studies motions (translations, rotations, reflections). | Symmetry, isometries. |
| Differential | Uses calculus to examine curves & surfaces. | Curvature, surface area via integrals. |
These axioms form the logical foundation for most elementary geometry.
| Quadrilateral | Properties |
|---|---|
| Parallelogram | Opposite sides parallel & equal; opposite angles equal. |
| Rectangle | Parallelogram with all right angles. |
| Rhombus | Parallelogram with all sides equal. |
| Square | Both rectangle and rhombus; all sides equal |