The Mathletes
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  • Chapter 1 Foundations of Geometry
    • 1.1 understanding Points, Lines and Planes
      • 1.2 Measuring and Constructing Segments
        • 1.3 Measuring and Constructing Angles
          • 1.4 Pairs of Angles
            • 1.5 Using Formulas in Geometry
              • 1.6 Midpoint and Distance in the Coordinate Plane
                • 1.7 Transformations in the Coordinate Plane
                • Chapter 2 Geometric Reasoning
                  • 2.1 Using Inductive Reasoning to Make Conjectures
                    • 2.2 Conditional Statements
                      • 2.3 Using Deductive Reasoning to Verify Conjectures
                        • 2.4 Biconditional Statements and Definitions
                          • 2.5 Algebraic Proof
                            • 2.6 Geometric Proof
                              • 2.7 Flowchart and Paragraph Proofs
                              • Chapter 3 Parallel and Perpendicular Lines
                                • 3.1 Lines and Angles
                                  • 3.2 Angles Formed by Parallel Lines and Transversals
                                    • 3.3 Proving Lines Parallel
                                      • 3.4 Perpendicular Lines
                                        • 3.5 Slopes of Lines
                                        • Chapter 4 Triangle Congruence
                                          • 4.1 Classifying Triangles
                                            • 4.2 Angle Relationships in Triangles
                                              • 4.4 Triangle Congruence: SSS and SAS
                                                • 4.5 Triangle Congruence: ASA, AAS, and HL
                                                  • 4.6 Triangle Congruence: CPCTC
                                                  • Chapter 5 Properties and Attributes of Triangles
                                                    • 5.1 Perpendicular and Angle Bisectors
                                                      • 5.3 Medians and Altitudes of Triangles
                                                        • 5.4 The Triangle Midsegment Theorem
                                                          • 5.5 Indirect Proof and Inequalities in One Triangle
                                                            • 5.6 Inequalities in 2 Triangles
                                                              • 5.7 The Pythagorean Theorem
                                                                • 5.8 Applying Special Right Triangles

                                                                1.1 Understanding Points, Lines and Planes

                                                                Point: Location without size
                                                                Line: Straight path without thickness, extends forever
                                                                Plane: Flat surface without thickness, extends forever
                                                                Segment: Part of line consisting of two points, and all points in between
                                                                Endpoint: A point at one end of a segment or the starting point of a ray
                                                                Ray: Part of a line that starts at an endpoint and extends forever in one direction
                                                                Opposite Ray: 2 rays that have a common endpoint

                                                                Postulate 1-1-1 Through any 2 points, there is exactly one line
                                                                Postulate 1-1-2 Through any 3 non-colinear points, there is exactly one plane containing them
                                                                Postulate 1-1-3 If 2 points lie in a plane, then the line containing those points lies in the plane

                                                                Postulate 1-1-4 If 2 lines intersect, then they intersect at exactly one point
                                                                Postulate 1-1-5 If 2 planes intersect, they do so at one line

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