## Elementary Geometry from an Advanced StandpointStudents can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24. |

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### Contents

The Algebra of the Real Numbers | 1 |

Incidence Geometry in Planes and Space | 43 |

Separation in Planes and Space | 72 |

Copyright | |

24 other sections not shown

### Common terms and phrases

AABC ADEF algebraic altitude angles are congruent Archimedean postulate base belongs called Chapter circular sector collinear congruent contains convex convex polygonal convex set coordinate system defined definition denoted dihedral angle distance edge element end points equation equivalent Euclid Euclidean geometry exactly exterior angle exterior angle theorem Figure finite following theorem formula area Given AABC graph half planes holds hyperbolic geometry inequality intersects isometry L-line LABC LEMMA length mathematics means measure merely one-to-one correspondence opposite sides ordered field parallel postulate point Q polygonal region polynomial positive integers positive number preserve Problem Set PROOF Pythagorean theorem radius rational numbers real number system rectangle Restatement right angle right triangle root ruler and compass ruler postulate Saccheri quadrilateral satisfies Section segment sequence square Suppose surd surd plane synthetic tangent tion triangular regions upper bound vertices