## The Foundations of GeometryThis text comfortably serves as a bridge between lower-level mathematics courses (calculus and linear algebra) and upper-level courses (real analysis and abstract algebra). It fully implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers. Foundations of Geometry particularly teaches good proof-writing skills, emphasises the historical development of geometry, and addresses certain issues concerning the place of geometry in human culture. |

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### Contents

Axiomatic Systems and Incidence Geometry | 17 |

Theorems Proofs and Logic | 31 |

The Axioms of Plane Geometry | 52 |

Copyright | |

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### Common terms and phrases

AA BC AABC Alternate Interior Angles angle measure angle of parallelism angle sum Archimedean Property assume asymptotically parallel axiomatic system axioms chapter Choose a point circle collinear common perpendicular congruent Construction Problem Corollary corresponding Crossbar Theorem curve defect defined definition disk model distance equal equilateral Euclid's Proposition Euclidean geometry Euclidean Parallel Postulate example Exercise Exterior Angle Theorem external point FIGURE Gaussian curvature geodesic glide reflection half-plane hyperbolic geometry hyperbolic plane Incidence Axiom incidence geometry inscribed Interior Angles Theorem intersect isometry LB AC LBAC Lemma Let AABC lies mathematics midpoint neutral geometry parallel lines parallelogram perpendicular bisector Poincare disk polygonal region proof of Theorem properties Protractor Postulate prove Pythagorean Theorem RAA hypothesis real numbers rectangle right angle Ruler Postulate Saccheri quadrilateral segment similar triangles statement straight line straightedge surface tangent torus transformation triangle AABC Triangle Theorem triangular region undefined terms unique vertex vertices