Geometry

  1. Coordinate Geometry
    1. The Coordinate System
      1. Cartesian Coordinate Plane
        1. Axes and Origin
          1. Quadrants
            1. Plotting Points
              1. Ordered Pairs
              2. Distance and Midpoint
                1. Distance Formula
                  1. Derivation from Pythagorean Theorem
                  2. Midpoint Formula
                    1. Derivation and Applications
                      1. Finding Endpoints
                    2. Slope
                      1. Definition of Slope
                        1. Slope Formula
                          1. Interpreting Slope
                            1. Positive and Negative Slope
                              1. Zero and Undefined Slope
                              2. Slope as Rate of Change
                              3. Equations of Lines
                                1. Slope-Intercept Form
                                  1. y = mx + b
                                    1. Identifying Slope and y-intercept
                                    2. Point-Slope Form
                                      1. y - y₁ = m(x - x₁)
                                      2. Standard Form
                                        1. Ax + By = C
                                          1. Converting Between Forms
                                          2. Horizontal and Vertical Lines
                                          3. Parallel and Perpendicular Lines
                                            1. Slopes of Parallel Lines
                                              1. Equal Slopes Condition
                                              2. Slopes of Perpendicular Lines
                                                1. Negative Reciprocal Condition
                                                2. Writing Equations of Parallel Lines
                                                  1. Writing Equations of Perpendicular Lines
                                                  2. Coordinate Proofs
                                                    1. Placing Figures in Coordinate Plane
                                                      1. Proving Properties Using Coordinates
                                                        1. Proving Parallelism
                                                          1. Proving Perpendicularity
                                                            1. Proving Congruence
                                                              1. Proving Collinearity
                                                              2. Finding Areas Using Coordinates
                                                                1. Shoelace Formula
                                                                  1. Using Basic Area Formulas
                                                                2. Circles in the Coordinate Plane
                                                                  1. Standard Form of Circle Equation
                                                                    1. Finding Center and Radius
                                                                      1. Writing Circle Equations
                                                                        1. Graphing Circles

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                                                                      11. Three-Dimensional Geometry

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                                                                      1. Foundations of Euclidean Geometry