Geometry

  1. Triangles
    1. Triangle Fundamentals
      1. Definition of a Triangle
        1. Parts of a Triangle
          1. Sides
            1. Angles
              1. Vertices
              2. Triangle Notation
                1. Interior and Exterior of a Triangle
                2. Classifying Triangles
                  1. Classification by Side Length
                    1. Scalene Triangle
                      1. Isosceles Triangle
                        1. Equilateral Triangle
                        2. Classification by Angle Measure
                          1. Acute Triangle
                            1. Right Triangle
                              1. Obtuse Triangle
                                1. Equiangular Triangle
                              2. Angle Relationships in Triangles
                                1. Triangle Sum Theorem
                                  1. Statement and Proof
                                  2. Exterior Angle Theorem
                                    1. Statement and Proof
                                      1. Remote Interior Angles
                                      2. Third Angle Theorem
                                      3. Triangle Congruence
                                        1. Definition of Congruent Triangles
                                          1. Corresponding Parts of Congruent Triangles
                                            1. CPCTC Theorem
                                              1. Side-Side-Side Congruence
                                                1. SSS Postulate
                                                  1. Applications and Proofs
                                                  2. Side-Angle-Side Congruence
                                                    1. SAS Postulate
                                                      1. Applications and Proofs
                                                      2. Angle-Side-Angle Congruence
                                                        1. ASA Postulate
                                                          1. Applications and Proofs
                                                          2. Angle-Angle-Side Congruence
                                                            1. AAS Theorem
                                                              1. Applications and Proofs
                                                              2. Hypotenuse-Leg Theorem
                                                                1. HL Theorem for Right Triangles
                                                                  1. Applications and Proofs
                                                                  2. Using Congruence in Proofs
                                                                  3. Isosceles and Equilateral Triangles
                                                                    1. Isosceles Triangle Theorem
                                                                      1. Base Angles Theorem
                                                                        1. Proof and Applications
                                                                        2. Converse of Isosceles Triangle Theorem
                                                                          1. Properties of Equilateral Triangles
                                                                            1. All Angles are 60 Degrees
                                                                              1. All Sides are Congruent
                                                                              2. Equilateral Triangle Theorems
                                                                              3. Special Segments in Triangles
                                                                                1. Perpendicular Bisectors
                                                                                  1. Definition and Construction
                                                                                    1. Perpendicular Bisector Theorem
                                                                                      1. Circumcenter
                                                                                        1. Definition and Properties
                                                                                          1. Constructing the Circumcenter
                                                                                            1. Circumcircle
                                                                                          2. Angle Bisectors
                                                                                            1. Definition and Construction
                                                                                              1. Angle Bisector Theorem
                                                                                                1. Incenter
                                                                                                  1. Definition and Properties
                                                                                                    1. Constructing the Incenter
                                                                                                      1. Incircle
                                                                                                    2. Medians
                                                                                                      1. Definition and Construction
                                                                                                        1. Properties of Medians
                                                                                                          1. Centroid
                                                                                                            1. Definition and Properties
                                                                                                              1. Constructing the Centroid
                                                                                                                1. Centroid Theorem
                                                                                                              2. Altitudes
                                                                                                                1. Definition and Construction
                                                                                                                  1. Properties of Altitudes
                                                                                                                    1. Orthocenter
                                                                                                                      1. Definition and Properties
                                                                                                                        1. Constructing the Orthocenter
                                                                                                                    2. Triangle Inequality Theorem
                                                                                                                      1. Statement of the Theorem
                                                                                                                        1. Proof of Triangle Inequality
                                                                                                                          1. Applications
                                                                                                                            1. Determining Possible Triangles
                                                                                                                              1. Finding Range of Third Side
                                                                                                                              2. Converse Applications

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                                                                                                                            4. Logic and Geometric Proofs

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                                                                                                                            6. Right Triangles and Trigonometry