Plane Geometry

plane geometry banner 2Plane geometry, also known as two-dimensional geometry, is a branch of mathematics that focuses on the properties and relationships of points, lines, angles, and shapes in a two-dimensional plane.  It is a fundamental area of study in mathematics and has many practical applications in fields such as engineering, architecture, physics, and computer graphics.  Plane geometry begins with basic concepts such as points, lines, and planes, and then progresses to more complex topics such as angles, triangles, polygons, circles, and conic sections.  The study of plane geometry involves the use of axioms and postulates to prove theorems and derive formulas that describe the properties and relationships of various geometric shapes and figures.  Overall, plane geometry provides a foundation for understanding the geometry of the physical world around us and plays a crucial role in many areas of science, engineering, and technology.

Some important concepts in plane geometry include:

  • Parallel lines and their relationship to angles and transversals
  • Congruent and similar figures
  • Properties of triangles, such as the Pythagorean theorem, and the relationship between angles and side lengths
  • Properties of circles, such as the relationship between angles, arcs, and chords
  • The use of coordinate geometry to describe the location and properties of points, lines, and shapes on a plane.


Science Branches

Formal Science
Pure Mathematics
  • Affine Geometry
  • Algebraic Geometry
  • Algebraic Topology
  • Analytic Geometry
  • Convex Geometry
  • Differential Geometry
  • Differential Topology
  • Discrete Geometry
  • Euclidean Geometry
  • General Topology
  • Geometric Topology
  • Non-Euclidean Geometry
  • Projective Geometry
  • Topology

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Nomenclature & Symbols

Plane Geometry Types

  • Polygon  -  A closed plane figure for which all edges are line segments and not necessarly congruent.
    • Concave Polygon  -  A polygon where one or more angles are greater than 180° and some vertices point inward.
    • Convex Polygon  -  A a polygon where all interior angles are less than 180° and all vertices point outward.
    • Irregular Polygon  -  A polygon where all edge and angles are not the same.  It can be concave or convex.
    • Regular Polygon  -  A polygon where all edges are congruent and all angles are congruent.
    • Self-intersecting Polygon  -  A polygon where one or more edges cross over another.
      • Triangle  -  A polygon with 3 edges.
      • Quadrilateral  -  A polygon with 4 edge.
        • Acute Trapezoid  -  A trapezoid has two adjacent acute angles on its longer base edge.
        • Isosceles Trapezoid  -  A trapezoid with only one pair of parallel edges and having base angles that are the same.
        • Kite  -  A quadrilateral with two pairs of adjacent edges that are congruent.
        • Obtuse Trapezoid  -  A trapezoid with one acute and one obtuce angle on each base.
        • Parallelogram  -  A quadrilateral with two pairs of parallel opposite edges.
        • Rectangle  -  A quadrilateral with two pair of parallel edges.
        • Rhombus  -  A parallelogram with four congruent edges.
        • Right Trapezoid  -  A trapezoid with only one pair of parallel edges and two adjacent right angles.
        • Rounded Corner Rectangle  -  A quadrilateral with two pair of parallel edges and rounded corners.
        • Self-intersecting Rectangle  -  One edge crosses over another.
        • Square  -  A quadrilateral with four equal edge lengths and 90° interior angles.
        • Trapezoid  -  A quadrilateral that has a pair of parallel opposite edges.
        • Tri-equilateral Trapezoid  -  A trapezoid with only one pair of parallel edges and having base angles that are the same with three congruent edges.
      • Pentagon  -  A polygon with 5 edges.
      • Hexagon  -  A polygon with 6 edges.
      • Heptagon  -  A polygon with 7 edges.
      • Octagon  -  A polygon with 8 edges.
      • Nonagon  -  A polygon with 9 edges.
      • Decagon  -  A polygon with 10 edges.
      • Hendecagon  -  A polygon with 11 edges.
      • Dodecagon  -  A polygon with 12 edges.
      • Triskaidecagon  -  A polygon with 13 edges.
      • Tetrakaidecagon  -  A polygon with 14 edges.
      • Pentadecagon  -  A polygon with 15 edges.
      • Hexakaidecagon  -  A polygon with 16 edges.
      • Heptadecagon  -  A polygon with 17 edges.
      • Octakaidecagon  -  A polygon with 18 edges.
      • Enneadecagon  -  A polygon with 19 edges.
      • Icosagon  -  A polygon with 20 edges.
      • Triacontagon  -  A polygon with 30 edges.
      • Tetracontagon  -  A polygon with 40 edges.
      • Pentacontagon  -  A polygon with 50 edges.
      • Hexacontagon  -  A polygon with 60 edges.
      • Heptacontagon  -  A polygon with 70 edges.
      • Octacontagon  -  A polygon with 80 edges.
      • Enneacontagon  -  A polygon with 90 edges.
      • Hectogon  -  A polygon with 100 edges.
      • Chiliagon  -  A polygon with 1,000 edges.
      • Myriagon  -  A polygon with 10,000 edges.


Geometric Properties of Structural Shapes


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3 Connecting Circles
3 Overlapping Circles
4 Connecting Circles
Acute Trapezoid
Annulus of a Circle

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