Geometry

  1. Geometric Relationships

    1. Lines and Planes
    2. Prisms, Pyramids, Cylinders, Cones, Spheres, Platonic Solids *
    3. Polygons – Interior and Exterior Angles *
    4. Multiple Choice Practice – Geometric Relationships (interactive & hardcopy)
  2. Constructions

    1. Constructions: Copy, Bisect, Perpendicular, Parallel, Isosceles, Equilateral
    2. Concurrence of Medians, Altitudes, Angle Bisectors, Perpendicular Bisectors *
    3. Multiple Choice Practice – Constructions (interactive & hardcopy)
  3. Locus

    1. The Basic Locus Theorems
    2. Compound Loci
    3. Multiple Choice Practice – Locus (interactive & hardcopy)
  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
    18. Multiple Choice Practice – Triangles (interactive & hardcopy)
    19. Multiple Choice Practice – Parallels and Quadrilaterals (interactive & hardcopy)
    20. Multiple Choice Practice – Circles (interactive & hardcopy)
      1. Why Study Proofs?
      2. Notation
      3. Vocabulary Resources
      4. Theorem/Properties
  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 (interactive & hardcopy)
    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
    7. Multiple Choice Practice – Coordinate Geometry (interactive & hardcopy)