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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.

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• Preface(p. vii)
• List of Numbered Figures(p. xi)
• List of Classroom Connections(p. xiii)
• List of Classroom Discussions(p. xv)
• 1 Euclid's Geometry(p. 1)
• 1.1 Euclid's Postulates and Common Notions(p. 2)
• 1.2 Using Logic(p. 3)
• 1.3 Notation and Measurement(p. 11)
• 1.4 Polygons and Solids(p. 19)
• 1.5 Measuring the Earth's Radius(p. 28)
• Chapter 1 Review(p. 31)
• Chapter 1 Review Exercises(p. 33)
• Related Reading for Chapter 1(p. 33)
• 2 Congruent Figures, Areas, and Volumes(p. 35)
• 2.1 Congruent Triangles(p. 35)
• 2.2 Parallel Lines(p. 48)
• 2.3 Quadrilaterals(p. 57)
• 2.4 Areas of Figures(p. 61)
• 2.5 Circles(p. 69)
• 2.6 Volumes and Surface Areas(p. 75)
• Chapter 2 Review(p. 86)
• Chapter 2 Review Exercises(p. 88)
• Related Reading for Chapter 2(p. 90)
• 3 Similarity(p. 92)
• 3.1 Similar Polygons(p. 92)
• 3.2 Applications of Similar Triangles(p. 98)
• 3.3 Pythagorean Theorem(p. 106)
• 3.4 Area and Perimeter of Similar Figures(p. 116)
• 3.5 Similarity for More General Figures(p. 123)
• Chapter 3 Review(p. 127)
• Chapter 3 Review Exercises(p. 128)
• Related Reading for Chapter 3(p. 131)
• 4 Rigid Motions and Symmetry(p. 132)
• 4.1 Reflections Over Lines and Orientation(p. 133)
• 4.2 Translations, Rotations, and Glide-Reflections(p. 139)
• 4.3 Symmetries(p. 146)
• 4.4 Isometries in Space(p. 151)
• Chapter 4 Review(p. 157)
• Chapter 4 Review Exercises(p. 159)
• Related Reading for Chapter 4(p. 161)
• 5 Vectors and Transformations(p. 162)
• 5.1 Vectors as Oriented Line Segments(p. 162)
• 5.2 Representing Vectors with Coordinates(p. 167)
• 5.3 Matrices(p. 171)
• 5.4 Transformations Using Matrices(p. 179)
• 5.5 Isometries and Orthogonal Matrices(p. 189)
• 5.6 Isometries and Complex Numbers(p. 193)
• Chapter 5 Review(p. 202)
• Chapter 5 Review Exercises(p. 204)
• Related Reading for Chapter 5(p. 208)
• 6 Three Other Geometries(p. 209)
• 6.1 Taxicab Geometry(p. 210)
• 6.2 Spherical Geometry(p. 216)
• 6.3 Hyperbolic Geometry(p. 229)
• Chapter 6 Review(p. 234)
• Chapter 6 Review Exercises(p. 236)
• Related Reading for Chapter 6(p. 238)
• Appendix I Geometer's Sketchpad(p. 239)
• Appendix II Euclid's Assumptions(p. 248)
• Appendix III Selected Geometry Formulas(p. 252)
• Glossary(p. 255)
• Answers and Hints for Odd Exercises(p. 272)
• Photo Credits(p. 291)
• Index(p. 293)