Plane Geometry

  1. Introduction to Geometry                                                                        * Days
    1. Basic Topics: point, line, ray etc.
    2. Measurement of Segments and Angles
    3. Collinearity, Betweenness, and Assumptions
    4. Two Column Proof Format
    5. Division of Angles and Segments
    6. Deductive Structure
  2. Basic Concepts and Proofs                                                                      * Days
    1. Perpendicularity
    2. Complementary and Supplementary Angles
    3. Drawing Conclusions
    4. Congruent Complements and Supplements
    5. Addition and Subtraction Properties
    6. Multiplication and Division Properties
    7. Transitive Property
    8. Vertical Angles
  3. Congruent Triangles                                                                                * Days
    1. Congruent Figures
    2. SSS, SAS, and ASA Postulates
    3. CPCTC
    4. Triangle Classification
    5. HL Postulate
  4. Lines in the Plane                                                                                    * Days
    1. Perpendicular Bisector Theorems
    2. Parallel Lines
    3. Slope
  5. Parallel and Perpendicular Lines                                                           7 Days
    1. Proving Lines are Parallel
    2. Congruent Angles with Parallel Lines
  6. Quadrilaterals                                                                                          * Days
    1. Types of Quadrilaterals
    2. Properties of Quadrilaterals
    3. Proving a Quadrilateral is a Parallelogram
    4. Proving Other Quadrilaterals
End of First Semester
  1. Polygons                                                                                                    * Days
    1. Formulas Involving Polygons – (Sum of interior/exterior angles, # diagonals)
    2. Regular Polygons – (measure of each exterior angle of a regular polygon formula)
  2. Similar Polygons                                                                                       * Days
    1. Ratio and Proportion – (Means-Extremes Products and Ratios Theorem)
    2. Similarity – (Similar Polygons)
    3. Methods of Proving Triangles Similar – (AAA, AA, SSS~, SAS~)  
    4. Congruences and Proportions in Similar Triangles
    5. Three Theorems Involving Proportions – (Angle Bisector Theorem)
  3. The Pythagorean Theorem                                                                     * Days
    1. Altitude-On-Hypotenuse Theorems
    2. Geometry’s Most Elegant Theorem – (The Pythagorean Theorem)
    3. The Distance Formula
    4. Families of Right Triangles
    5. Special Right Triangles – (30-60-90 and 45-45-90)

     Trigonometry

    1. Introduction to Trigonometry – (Three Trigonometric Ratios
    2. Trigonometric Ratios – (Angle of Depression and Elevation)
  1. Circles                                                                                                     * Days
    1. The Circle – (Area, Circumference, Radius-Chord Relationships)
    2. Congruent Chords
    3. Arcs of a Circle – (Relating Congruent Arcs, Chords, and Central Angles)
    4. Secants and Tangents – (Two Tangent Theorem, Common Tangents, Walk-Around Problems
    5. Arcs Related to a Circle – Inscribed, Tangent-Chord, Chord-Chord, Secant-Secant, Secant-Tangent, Tangent-Tangent)
    6. Inscribed And Circumscribed Polygons
    7. The Power Theorems – Chord-Chord, Tangent Secant, Secant-Secant
    8. Circumference and Arc Length
  2. Area                                                                                                         * Days
    1. Understanding Area – Rectangle, Square
    2. Areas of Parallelograms and Triangles
    3. The area of a Trapezoid
    4. Areas of Rhombus
    5. Areas of Regular Polygons – Equilateral Triangle, Apothem
    6. Areas of Circles, Sectors and Segments
  3. Surface Areas and Volume                                                                     * Days
    1. Surface Areas of Prisms – lateral and total surface area
    2. Volumes of Prisms and Cylinders
End of Second Semester

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Last updated: January 25, 2008