Euclidean and Transformational Geometry: A Deductive Inquiry

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Jones & Bartlett Learning, Feb 12, 2008 - Mathematics - 371 pages
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Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.
 

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Contents

Prologue
1
Congruence Constructions and the Parallel Postulate
9
Circles
75
Area and the Pythagorean Theorem
115
Similarity
155
Isometries and Size Transformations
237
Composition of Transformations
283
More Recent Discoveries
317
Basic Notions
343
Selected Hints and Answers
355
References
365
Index
367
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