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.

Plane Geometry Types

• Circle  -   All points are at a fixed equal distance from a center point.
  
  • 3 Overlapping Circle  -  Equal length arcs connecting at the vertices of three overlapping circles.
  • 3 Connecting Circle  -  Three equal length arcs connecting at the vertices bound by circles.
  • 4 Connecting Circle  -  Four equal length arcs connecting at the vertices bound by circles.
  • Annulus of a Circle  -  The area between two concentric circles.
  • Arc Length of a Circle  -  A sector is a fraction of the area of a circle.
  • Area of a Circle  -
  • Chord of a Circle  -  An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.
  • Circle Corner  -  A right triangle having acute vertices on a circle with the hypotenuse outside the circle.
  • Circumference of a Circle  -
  • Diameter of a Circle  -  A circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle.
  • Half Circle  -  Half of the interior of a circle having a straight chord and an arc.
  • Hollow Circle  -  Two circles each having all points on each circle at a fixed equal distance from a center point.
  • Quarter Circle  -  A part of the interior of a circle having two radius boundries at a 90° angle and an arc.
  • Radius of a Circle  -  A line segment between the center point and a point on a circle or sphere.
  • Second Moment of Area of a Circle  -
  • Sector of a Circle  -  A part of the interior of a circle having two radius boundries and an arc.
  • Segment of a Circle  -  An interior part of a circle bound by a chord and an arc.
  • Thin Wall Circle  -  Two circles each having all points on each circle at a fixed equal distance from a center point.
  • Torsional Constant of a Circle  -

• Ellipse  -  A two-dimensional figure with a conic section or a stretched circle.
  
  • Catenart Curve  -  Has a u-shaped curve and can be represented by a hanging chain or cable under its own weight and supported only at it's ends.
  • Foci of an Ellipse  -  A point used to define the conic section.
  • Hollow Ellipse  -  Two ellipses with a conic section or a stretched circle.
  • Sector of an Ellipse  -  A part of the interior of an ellipse having two radius boundries and an arc.
  • Segment of an Ellipse  -  An interior part of a ellipse bound by a chord and an ellipse.
  • Semi-major and Semi-minor Axis of an Ellipse  -

• 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.
      
      • Acute Triangle  -  Has three angles less than 90°.
      • Equilateral Triangle  -  Has three edges that are the same length and all edges and angles are congruent.
      • Isosceles Triangle  -  Has two edges that are the same length or at least two congruent edges.
      • Oblique Triangle  -  Is tilted at an angle, not horizontal or vertical.
      • Obtuse Triangle  -  Has one of the three angles more than 90°.
      • Right Isosceles Triangle  -  Has one edge a right 90° interior angle and the other two angles are 45°.
      • Right Triangle  -  Has one edge a right 90° interior angle.
      • Scalene Triangle  -  All three edges are different lengths and all three angles are different angles.
    • 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.
      • Regular Pentagon  -  A polygon with 5 congruent edges.
    • Hexagon  -  A polygon with 6 edges.
      • Regular Hexagon  -  A polygon with 6 congruent edges.
    • Heptagon  -  A polygon with 7 edges.
      • Regular Heptagon  -  A polygon with 7 congruent 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

• Circle
• Circle Sector
• Circle Segment
• Cross
• Half Circle
• Hollow Circle
• Hollow Rectangle
• Quarter Circle
• Rectangle
• Rectangular Angle
• Regular Polygon
• Rotating Rectangle
• Square
• Square Angle
• Square Channel
• Square Diamond
• Square I Beam
• Square T Beam
• Tapered Channel
• Tapered I Beam
• Tapered T Beam
• Thin Wall Circle
• Thin Wall Rectangle
• Unequal I Beam
• Zed