Plane Geometry

Plane geometry is a two dimensional figure, also called planar geometry, with edges.  The edges are line segments or edges and curve segments or arcs, all lying on a flat plane.

Mathematic Symbols and Examples

Plane Geometry Types

  • Circle  -   All points are at a fixed equal distance from a center point.  See [ 1 ]
    • Circle Arc Triangle  -  Three equal length arcs bound by circles.
    • Circle Arc Square  -  Four equal length arcs bound by circles.
    • Circle Corner  -  A right triangle having acute vertices on a circle with the hypotenuse outside the circle.
    • Circle Sector  -  A part of the interior of a circle having two radius boundries and an arc.
    • Circle Segment  -  An interior part of a circle bound by a chord and an arc.  See [ 1 ]
    • Half Circle  -  Half of the interior of a circle having a straight chord and an arc.  See [ 1 ]
    • Hollow Circle  -  Two circles each having all points on each circle at a fixed equal distance from a center point.  See [ 1 ]
    • Quarter Circle  -  A part of the interior of a circle having two radius boundries at a 90° angle and an arc.  See [ 1 ]
    • Thin Wall Circle  -  Two circles each having all points on each circle at a fixed equal distance from a center point.  See [ 1 ]
  • Ellipse  -  A two-dimensional figure with a conic section or a stretched circle.
    • Ellipse Sector  -  A part of the interior of an ellipse having two radius boundries and an arc.
    • Ellipse Segment  -  An interior part of a ellipse bound by a chord and an ellipse.
    • Hollow Ellipse  -  Two ellipses with a conic section or a stretched circle.
  • 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.  See [ 1 ]
        • 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.  See [ 1 ]
        • 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.
     
  • Structural Steel Shapes
    • Cross  -  Two rectangles that intersect perpendicular at a center point.  See [ 1 ]
    • Hollow Rectangle  -  A quadrilateral with two pair of parallel edges.  See [ 1 ]
    • Rectangular Angle  -  Two unequal rectangles that intersect at a 90° angle at one end each.  See [ 1 ]
    • Square Angle  -  Two rectangles that intersect at a 90° angle at one end each.  See [ 1 ]
    • Square Channel  -  Three rectangles that intersect at 90° angles at each end of one rectangle.  See [ 1 ]
    • Square I Beam  -  Three rectangles, two that intersect at the center at 90° angles to the end of one rectangle.  See [ 1 ]
    • Square T Beam  -  Two rectangles, one intersects at the center at 90° angles to the end of one rectangle.  See [ 1 ]
    • Thin Wall Rectangle  -  A quadrilateral with two pair of parallel edges.  See [ 1 ]
    • Tapered Channel  -
    • Tapered I Beam  -
    • Tapered T Beam  -
    • Unequal I Beam  -
    • Zed  -  Three rectangles, two that intersect at a 90° angle to the third one at end each at different directions.  See [ 1 ]
     

[ 1 ] See Geometric Properties of Structural Shapes.

 

Display #
Title
Acute Trapezoid
Annulus
Arc Length of a Circle
Circle
Circle Arc Square
Circle Arc Triangle
Circle Corner
Circle Sector
Circle Segment
Concave Polygon