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What kinds of figures are studied in Euclidean plane geometry?

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Three theorems of congruent triangles — Euclidean geometry This diagram depicts three basic theorems that triangles are congruent—that is, they are of equal shape and size—if: (1) two sides and the included angle are equal, designated SAS; (2) two angles and the included side are equal, designated ASA; or (3) all three sides are equal, designated SSS.

Euclidean plane geometry focuses on the study of figures defined by axioms and theorems, primarily using a ruler and compass for constructions. The fundamental elements and figures studied include:1

Basic Elements: Points (which have no parts) and lines (lengths without breadth). These include line segments, which connect two points, and rays, which extend indefinitely from a single point.23
Angles: Defined as the inclination between two straight lines.2
Circles: Plane figures consisting of all points at a fixed distance (radius) from a center. This includes related components like chords, diameters, and semicircles.24
Polygons: Closed figures formed by a set of connected line segments. These include:5
- Triangles: Three-sided polygons.5
- Quadrilaterals: Four-sided polygons, such as squares (a type of regular quadrilateral) and rectangles.65
- Regular Polygons: Polygons with equal sides and angles, such as equilateral triangles and squares.65

These figures serve as the basis for exploring geometric properties, such as similarity, congruence, and distance, often calculated using the Pythagorean theorem.147