Geometry

Castle Learning Online's Geometry includes a review of basic geometric terms often introduced in middle schools and builds up to a more comprehensive treatment of plane figures, including area and perimeter problems, loci, coordinate geometry, transformations and symmetry; and three-dimensional figures, including surface area and volume. The course also includes step-by-step formal and informal proof-building questions concentrating on the five congruence techniques, similar triangles and proportions, indirect proof techniques, circle proofs, and coordinate geometry proofs.

Units: (click to view Sections)

1. Angles, Triangles, and other Polygons
   
   Sections:
   

   1. Angles (including supplementary, complementary, and vertical)
   2. Parallel Lines with a Transversal
   3. Triangles (Similar, interior, and exterior angles)
   4. Triangle Inequality
   5. Properties of Quadrilaterals
   6. Parallelograms and Rectangles
   7. Rhombuses and Squares
   8. Trapezoids and other Polygons
   9. Area and Perimeter of Polygons
   10. Circles (Area and Circumference)
   11. Combinations of Figures
   12. Planes
   13. Geometry Probability
2. Three-dimensional figures
   
   Sections:
   

   1. Definitions and shapes
   2. Rectangular solids (cubes, boxes)
   3. Cylinders, Cones, Spheres
   4. Prisms and Pyramids
3. Constructions
   
   Sections:
   

   1. Constructions
   2. Triangle Centers (centroid, incenter, circumcenter, orthocenter)
4. Locus
   
   Sections:
   

   1. Medians, altitudes, angle bisectors, and perpendicular bisectors of triangles
   2. Compound loci
   3. Compound loci on coordinate plane
5. Logical Reasoning
   
   Sections:
   

   1. Truth value and negation
   2. Conjunction, disjunction, conditional, and biconditional
   3. Inverse, converse, and contrapositive (logically equivalent)
   4. Proofs
6. Triangle proofs
   
   Sections:
   

   1. Geometric definitions
   2. Five congruence techniques (SSS, SAS, ASA, AAS, HL, CPCTC)
   3. Similarity (AA AA)
   4. Inequality and Indirect
7. Right Triangles
   
   Sections:
   

   1. Proportions
   2. Pythagorean Theorem
8. Circles
   
   Sections:
   

   1. Relationships between arcs and angles (inscribed, exterior, interior, central)
   2. Length of Tangents, Secants, and Chords
   3. Circle proofs
   4. Equation of a circle
   5. Graph on the coordinate plane
9. Transformations
   
   Sections:
   

   1. Rotations, Reflections, Dilations, Translations (Rules), and Symmetry
   2. Isometry
   3. Compositions
   4. Graphing questions
10. Coordinate Geometry
    
    Sections:
    

    1. Introduction to coordinates and the coordinate plane
    2. Equation of a line (Slope and y-intercept)
    3. Equations of parallel and perpendicular lines
    4. Midpoint
    5. Distance
    6. Coordinate geometry proofs (triangles, parallelograms, trapezoids)
    7. System of equations solved graphically (linear, quadratic, and inequalities)
    8. Finding the area of polygons on coordinate plane
11. Enrichment Topics
    
    Sections:
    

    1. Logic (Truth tables and symbols)
    2. Conic Sections
    3. Right Triangle Trigonometry
    4. Equation of a Parabola

Themes:

1. Number Systems
2. Number Theory
3. Operations
4. Estimation
5. Equations and Inequalities
6. Patterns, Relations, and Functions
7. Geometry (angles, lines)
8. Trigonometry
9. Area, Volume, Perimeter (including polygons and circles)
10. Geometric Relationships
11. Transformational Geometry
12. Coordinate Geometry
13. Constructions
14. Locus
15. Informal Proofs
16. Formal Proofs
17. Units of Measurement
18. Tools and Methods
19. Logic

Attributes:

1. Diagram
2. Table
3. Graph
4. Word Problem
5. Proof
6. Construction
7. Fill-In