--- title: Plane Geometry - Basic Concepts, Shapes & Equations description: "Explore plane geometry: basic concepts like points, lines, angles, polygons (triangles, quadrilaterals), circles, and coordinate geometry." url: https://astra-ai.co/videos/plane-geometry/ locale: en type: video-topic keywords: - plane geometry - triangles - circles - angles published: 2026-10-01T09:46:20.194Z updated: 2026-10-04T21:53:04.595Z alternates: bg: https://astra-ai.co/bg/videos/ploska-geometriya/ br: https://astra-ai.co/br/videos/geometria-plana/ cs: https://astra-ai.co/cs/videos/rovinna-geometrie/ da: https://astra-ai.co/da/videos/plan-geometri/ de: https://astra-ai.co/de/videos/geometrie-in-der-ebene/ el: https://astra-ai.co/el/videos/epipedi-geometria/ en: https://astra-ai.co/videos/plane-geometry/ en-IN: https://astra-ai.co/en-IN/videos/plane-geometry/ en-PH: https://astra-ai.co/en-PH/videos/plane-geometry/ es: https://astra-ai.co/es/videos/geometria-plana/ es-AR: https://astra-ai.co/es-AR/videos/geometria-plana/ es-CL: https://astra-ai.co/es-CL/videos/geometria-plana/ es-PE: https://astra-ai.co/es-PE/videos/geometria-plana/ et: https://astra-ai.co/et/videos/tasandigeomeetria/ fi: https://astra-ai.co/fi/videos/tasogeometria/ fr: https://astra-ai.co/fr/videos/geometrie-plane/ hr: https://astra-ai.co/hr/videos/ravninska-geometrija/ hu: https://astra-ai.co/hu/videos/sikgeometria/ id: https://astra-ai.co/id/videos/geometri-bidang/ it: https://astra-ai.co/it/videos/geometria-piana/ ja: https://astra-ai.co/ja/videos/plane-geometry-ja/ km: https://astra-ai.co/km/videos/plane-geometry/ ko: https://astra-ai.co/ko/videos/plane-geometry-ko/ lo: https://astra-ai.co/lo/videos/lo-d640810d/ lt: https://astra-ai.co/lt/videos/plokscioji-geometrija/ lv: https://astra-ai.co/lv/videos/plaknes-geometrija/ ms: https://astra-ai.co/ms/videos/plane-geometry/ ms-BN: https://astra-ai.co/ms-BN/videos/geometri-satah/ mx: https://astra-ai.co/mx/videos/geometria-plana/ my: https://astra-ai.co/my/videos/my-d640810d/ nl: https://astra-ai.co/nl/videos/vlakke-geometrie/ no: https://astra-ai.co/no/videos/plan-geometri/ pl: https://astra-ai.co/pl/videos/geometria-plaska/ pt: https://astra-ai.co/pt/videos/geometria-plana/ pt-TL: https://astra-ai.co/pt-TL/videos/geometria-plana/ ro: https://astra-ai.co/ro/videos/geometrie-plana/ sk: https://astra-ai.co/sk/videos/rovinna-geometria/ sl: https://astra-ai.co/sl/videos/ravninska-geometrija/ sr: https://astra-ai.co/sr/videos/geometrija-ravni/ sv: https://astra-ai.co/sv/videos/plan-geometri/ th: https://astra-ai.co/th/videos/plane-geometry/ tr: https://astra-ai.co/tr/videos/duzlem-geometrisi/ uk: https://astra-ai.co/uk/videos/uk-topic-07/ vi: https://astra-ai.co/vi/videos/vi-topic-07/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-007/ zh-TW: https://astra-ai.co/zh-TW/videos/plane-geometry/ --- # Plane Geometry > Plane geometry studies shapes in two dimensions. This topic covers points, lines, angles, triangles, and circles. Plane geometry is a branch of mathematics that studies the properties and relationships between various geometric objects in a two-dimensional space. The basic elements of plane geometry include points, lines, angles, polygons, and circles. These objects have specific properties and laws that can be described using mathematical rules and formulas. ## BASIC CONCEPTS OF PLANE GEOMETRY A **point** is the fundamental building block of geometry, having no dimensions and representing a location in the plane. A **line** is an infinite collection of points extending in one direction. A **line segment** is a part of a line bounded by two points, while a **ray** is a part of a line that has a starting point and extends infinitely in one direction. **Angles** are geometric objects formed by two rays sharing a common endpoint (vertex). Based on their size, we distinguish: - **Acute angles:** smaller than 90 degrees. - **Right angles:** measure exactly 90 degrees. - **Obtuse angles:** larger than 90 degrees but smaller than 180 degrees. - **Straight angles:** measure exactly 180 degrees. Important relationships between angles include **complementary angles**, whose sum is 90 degrees, and **supplementary angles**, whose sum is 180 degrees. ## POLYGONS AND THEIR PROPERTIES A **polygon** is a geometric figure bounded by several straight sides. The most common polygons include triangles, quadrilaterals, pentagons, and other figures with more sides. **Triangles** are classified based on the length of their sides (equilateral, isosceles, and scalene) or based on their angles (right-angled, acute-angled, and obtuse-angled). A right-angled triangle has one angle equal to 90 degrees, for which the Pythagorean theorem applies, defining the relationship between the lengths of its sides. Among **quadrilaterals**, we distinguish parallelograms, rectangles, squares, and trapezoids, which have different properties regarding the parallelism and length of sides and the size of angles. A square is a special type of rectangle in which all sides are equal in length, and a rectangle has opposite sides of equal length and all angles equal (90 degrees). ## THE CIRCLE AND ITS COMPONENTS A **circle** is the set of all points in a plane that are equidistant from a central point. The distance from the center to any point on the circle is called the **radius**. The longest distance through the center is the **diameter**, which is equal to twice the radius. A **chord** is a line segment connecting two points on the circle, and an **arc** is a part of the circle between two points. A **central angle** is an angle whose vertex is at the center of the circle, and its corresponding arc has a length proportional to the size of the angle. In circle geometry, the **inscribed angle** is also often used; it has its vertex on the circle and is equal to half the measure of its intercepted (central) arc. ## EQUATIONS IN THE COORDINATE SYSTEM Plane geometry can also be addressed using coordinate geometry, where the position of points is determined using a coordinate system. The distance between two points A(x₁, y₁) and B(x₂, y₂) in the coordinate system is calculated by the formula: d = sqrt((x₂ – x₁)² + (y₂ – y₁)² ) The equation of a line in the plane is given in the form y = mx + b, where 'm' is the slope, determining the inclination of the line, and 'b' is the y-intercept of the line. If we know two points on the line, the slope can be calculated as m = (y₂ – y₁) / (x₂ – x₁). ## CONCLUSION Plane geometry is one of the fundamental branches of mathematics that allows for the analysis and study of figures and their properties. Its concepts are crucial for understanding spatial relationships and are the basis for further exploration of geometry in three dimensions and for use in analytical geometry. Understanding basic concepts such as angles, polygons, circles, and lines facilitates easier solving of geometric problems and broader application in mathematical and scientific disciplines.