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Cover image for Geometry connections
Title:
Geometry connections
Personal Author:
Series:
Connections in Mathematics Course for Teachers
Publication Information:
Upper Saddle River, NJ : Pearson Prentice Hall, 2006
ISBN:
9780131449268

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30000010129731 QA461 B34 2006 Open Access Book Book
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30000010144376 QA461 B34 2006 Open Access Book Book
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30000010144377 QA461 B34 2006 Open Access Book Book
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Summary

Summary

With challenging new standards-based middle school mathematics curricula now in place, future teachers need college-level mathematics courses that better prepare them for their professional careers. This handbook presents a rigorous review of college-level geometry, designed to equip middle grade mathematics teachers with the skills needed for teaching NCTM (National Council of Teachers of Mathematics) Standards-based curricula. Contains geometry which middle school mathematics teachers will actually have to teach, as well as additional material to deepen future teachers' knowledge and understanding of geometry. Demonstrate the presentation and use of geometry in the middle school to assist students in linking the typical college geometry course with the standards-based concepts taught by middle school teachers. Includes a variety of activities designed to deepen the connections between the geometry students are studying now and the geometry they will teach. For anyone interested in learning more about geometry.


Table of Contents

Prefacep. vii
List of Numbered Figuresp. xi
List of Classroom Connectionsp. xiii
List of Classroom Discussionsp. xv
1 Euclid's Geometryp. 1
1.1 Euclid's Postulates and Common Notionsp. 2
1.2 Using Logicp. 3
1.3 Notation and Measurementp. 11
1.4 Polygons and Solidsp. 19
1.5 Measuring the Earth's Radiusp. 28
Chapter 1 Reviewp. 31
Chapter 1 Review Exercisesp. 33
Related Reading for Chapter 1p. 33
2 Congruent Figures, Areas, and Volumesp. 35
2.1 Congruent Trianglesp. 35
2.2 Parallel Linesp. 48
2.3 Quadrilateralsp. 57
2.4 Areas of Figuresp. 61
2.5 Circlesp. 69
2.6 Volumes and Surface Areasp. 75
Chapter 2 Reviewp. 86
Chapter 2 Review Exercisesp. 88
Related Reading for Chapter 2p. 90
3 Similarityp. 92
3.1 Similar Polygonsp. 92
3.2 Applications of Similar Trianglesp. 98
3.3 Pythagorean Theoremp. 106
3.4 Area and Perimeter of Similar Figuresp. 116
3.5 Similarity for More General Figuresp. 123
Chapter 3 Reviewp. 127
Chapter 3 Review Exercisesp. 128
Related Reading for Chapter 3p. 131
4 Rigid Motions and Symmetryp. 132
4.1 Reflections Over Lines and Orientationp. 133
4.2 Translations, Rotations, and Glide-Reflectionsp. 139
4.3 Symmetriesp. 146
4.4 Isometries in Spacep. 151
Chapter 4 Reviewp. 157
Chapter 4 Review Exercisesp. 159
Related Reading for Chapter 4p. 161
5 Vectors and Transformationsp. 162
5.1 Vectors as Oriented Line Segmentsp. 162
5.2 Representing Vectors with Coordinatesp. 167
5.3 Matricesp. 171
5.4 Transformations Using Matricesp. 179
5.5 Isometries and Orthogonal Matricesp. 189
5.6 Isometries and Complex Numbersp. 193
Chapter 5 Reviewp. 202
Chapter 5 Review Exercisesp. 204
Related Reading for Chapter 5p. 208
6 Three Other Geometriesp. 209
6.1 Taxicab Geometryp. 210
6.2 Spherical Geometryp. 216
6.3 Hyperbolic Geometryp. 229
Chapter 6 Reviewp. 234
Chapter 6 Review Exercisesp. 236
Related Reading for Chapter 6p. 238
Appendix I Geometer's Sketchpadp. 239
Appendix II Euclid's Assumptionsp. 248
Appendix III Selected Geometry Formulasp. 252
Glossaryp. 255
Answers and Hints for Odd Exercisesp. 272
Photo Creditsp. 291
Indexp. 293
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