Geometry

  1. Geometric Relationships
    1. Lines and Planes
    2. Prisms, Pyramids, Cylinders, Cones, Spheres, Platonic Solids
    3. Polygons – Interior and Exterior Angles
  2. Constructions
    1. Constructions: Copy, Bisect, Perpendicular, Parallel, Isosceles, Equilateral
    2. Concurrence of Medians, Altitudes, Angle Bisectors, Perpendicular Bisectors
  3. Locus
    1. The Basic Locus Theorems
    2. Compound Loci
  4. Informal and Formal Proof
    1. Logic – Negation, Conjunction, Disjunction, Conditional , Biconditional, Truth
    2. Related Conditionals — Converse, Inverse, Contrapositive
    3. Writing a Proof – Direct Euclidean Proofs
    4. Writing a Proof – Indirect Euclidean Proofs
    5. Congruence of Triangles
    6. Angles and Triangles
    7. Isosceles Triangle Theorems
    8. Triangle Inequality Theorems
    9. Parallel Lines and Angles
    10. Quadrilaterals
    11. Mid-Segment (Mid-Line) of a Triangle
    12. Similarity of Triangles
    13. Mean Proportional in a Right Triangle
    14. Pythagorean Theorem and Converse
    15. Circles: Chords, Secants and Tangents
    16. Circles: Angles and Arcs
    17. Circles: Area of Sectors and Segments
  5. Transformational Geometry
    1. General “Transformation” Vocabulary for this Section
    2. Symmetry – Line, Plane, Point, Rotational – Intuitive
    3. Reflections – Line, Point
    4. Translations
    5. Dilations and Similarity
    6. Rotations
    7. Review of Transformation Information
    8. Compositions and Glide Reflections
    9. Multiple Choice Practice – Transformations
    10. Opening in a new window …
    11. Using the Graphing Calculator to Examine Reflections, Translations, Dilations
    12. Using the Graphing Calculator to Examine Rotations
  6. Coordinate Geometry
    1. Slopes and Equations of Lines
    2. Midpoint of a Line Segment
    3. Distance Formula
    4. Direct Analytic Proofs (Coordinate Geometry Proofs)
    5. Linear – Quadratic Systems *
    6. Circles