I. Geometry: The Study of Shapes

  1. What the… Geometry?  Really?
  2. Definitions in Geometry
  3. Known Implication: Elements of the Proof
  4. Angles: Complementary and supplementary
  5. Transitive and Substitution Properties
  6. Starting on Both Ends of the Problem

II. Triangles

  1. Three Types of Triangles
    1. Drafting the Right Triangle
  2. Areas of Triangles
  3. Solutions for All Sides and Angles
    1. Knowing only 3 Elements
  4. The Centroid, Bisectors and Centers
  5. Pythagorean Theorem

III. Congruence and Proportionality

  1. When Equality isn’t an Exact Non-Carbon Copy
  2. Dissection by means of Interior Triangles
  3. Projections through Parallelization
  4. Transversals

IV. Quadrilateral Shapes

  1. The 7 Quadrilateral Shapes with Symmetry
    1. The Kite
    2. The Parallelogram
    3. The Trapezoid
    4. The Rhombus
    5. The Rectangle
    6. The Isosceles Trapezoid
    7. The Square
  2. Specific Properties of the Quadrilaterals
    1. Areas, Angles, and Diagonals
  3. Quadrilateral Proofs

IV. Polygons

  1. Regular polygons
    1. Areas, Angles, and Diagonals
  2. Similar Shapes of Varied Dimensions
    1. Similar Triangles and Altitude-on-Hypotenuse
    2. Angle-Bisector Theorem

V. Circles

  1. Chords, Radii, and Diameters
  2. Central Angles and Arcs
    1. The Walk-Around Problem
    2. Determination of Arc Length
    3. Area of a Sector
    4. Area of a Circular Segment
  3. Angle-Arc Relations
    1. Angles On, Inside, and Outside a Circle

VI. 3-D Geometry

  1. Parallel and Perpendicular Lines and Planes
  2. Flat Top Figures: Areas and Volumes
    1. Boxes, Prisms, and Cylinders
  3. Pyramids and Cones: Areas and Volume

VII. Coordinate Geometry

  1. Distance and Midpoint Formulations
  2. Solving Problems Algebraically

VIII. Geometric Transformations

  1. Reflections
  2. Translations
  3. Rotations
  4. Developing the Loci of Points