1. Introduction to Geometry                                                                        15 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
   7. Statements of Logic
   8. Probability
2. Basic Concepts and Proofs                                                                      13 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                                                                                14 Days
   1. Congruent Figures
   2. SSS, SAS, and ASA Postulates
   3. CPCTC
   4. Overlapping Triangles
   5. Triangle Classification
   6. Angle-Side Theorems
   7. HL Postulate
4. Lines in the Plane                                                                                    12 Days
   1. Detour Proofs
   2. Proofs Without Diagrams
   3. Perpendicular Bisector Theorems
   4. Parallel Lines
   5. Slope
5. Parallel and Perpendicular Lines                                                         7 Days
   1. Proving Lines are Parallel
   2. Congruent Angles with Parallel Lines
6. Quadrilaterals                                                                                          9 Days
   1. Types of Quadrilaterals
   2. Properties of Quadrilaterals
   3. Proving a Quadrilateral is a Parallelogram
   4. Proving Other Quadrilaterals
7. Lines and Planes in Space                                                                       6 Days

   1. Intersecting Lines and Planes, Methods of Determining a Plane
   2. Perpendicularity of a Line and a Plane
   3. Properties Relating Lines and Planes 

8. Polygons                                                                                                    10 Days
   1. Triangle Application Theorems
   2. Two Proof-Oriented Triangle Theorems – (No-Choice Theorem, AAS)
   3. Formulas Involving Polygons – (Sum of interior/exterior angles, # diagonals)
   4. Regular Polygons – (measure of each exterior angle of a regular polygon formula)
9. Similar Polygons                                                                                       11 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 – (Side-Splitter Theorem, Angle Bisector Theorem)
10. The Pythagorean Theorem                                                                     17 Days
    1. Review of Radicals and Quadratic Equations
    2. Introduction to Circles
    3. Altitude-On-Hypotenuse Theorems
    4. Geometry’s Most Elegant Theorem – (The Pythagorean Theorem)
    5. The Distance Formula
    6. Families of Right Triangles
    7. Special Right Triangles – (30-60-90 and 45-45-90)
    8. The Pythagorean Theorem and Space Figures – (Rectangular Solid, and Regular Square Pyramid

Trigonometry

1. Introduction to Trigonometry – (Three Trigonometric Ratios
2. Trigonometric Ratios – (Angle of Depression and Elevation)

 

11. Circles                                                                                                     19 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. More Angle-Arc Theorems
    7. Inscribed And Circumscribed Polygons
    8. The Power Theorems – Chord-Chord, Tangent Secant, Secant-Secant
    9. Circumference and Arc Length
12. Area                                                                                                         10 Days
    1. Understanding Area – Rectangle, Square
    2. Areas of Parallelograms and Triangles
    3. The area of a Trapezoid – Median of a Trapezoid
    4. Areas of Kites and Related Figures – Rhombus
    5. Areas of Regular Polygons – Equilateral Triangle, Apothem
    6. Areas of Circles, Sectors and Segments
    7. Ratios of Areas
    8. Hero’s And Brahmagupta’s Formulas
13. Surface Areas and Volume                                                                6 Days
    1. Surface Areas of Prisms – lateral and total surface area
    2. Surface Area of Pyramids
    3. Surface Area of Circular Solids
    4. Volumes of Prisms and Cylinders
    5. Volumes of Pyramids and Cones
    6. Volumes of Spheres
14. Coordinate Geometry Extended                                                            13 Days
    1. Graphing Equations
    2. Equations of Lines
    3. Systems of Equations
    4. Graphing Inequalities
    5. Circles – Equation of Circle
    6. Coordinate-Geometry Practice