{"product_id":"college-geometry-with-geogebra-isbn-9781119718116","title":"College Geometry with GeoGebra","description":"\u003cp\u003eFrom two authors who embrace technology in the classroom and value the role of collaborative learning comes \u003ci\u003eCollege Geometry Using GeoGebra\u003c\/i\u003e, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry.\u003c\/p\u003e \u003cp\u003eEmphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, \u003ci\u003eCollege Geometry with GeoGebra \u003c\/i\u003eis an ideal resource for geometry courses for both mathematics and math education majors.\u003c\/p\u003e \u003cp\u003ePreface\u003c\/p\u003e \u003cp\u003eEspecially for Students\u003c\/p\u003e \u003cp\u003eNotes for Instructors\u003c\/p\u003e \u003cp\u003eOur Motivation, Philosophy, and Pedagogy\u003c\/p\u003e \u003cp\u003ePrerequisites and Chapter Dependencies\u003c\/p\u003e \u003cp\u003eAcknowledgments\u003c\/p\u003e \u003cp\u003eONEUsing GeoGebra\u003c\/p\u003e \u003cp\u003e1.1 Activities: Getting Started with GeoGebra\u003c\/p\u003e \u003cp\u003e1.2 Discussion: Exploring and Conjecturing\u003c\/p\u003e \u003cp\u003eSome GeoGebra Tips\u003c\/p\u003e \u003cp\u003eConstructing −→ Exploring −→ Conjecturing:\u003c\/p\u003e \u003cp\u003eInductive Reasoning\u003c\/p\u003e \u003cp\u003eLanguage of Geometry\u003c\/p\u003e \u003cp\u003eExplorations, Observations, Questions\u003c\/p\u003e \u003cp\u003eThe Family of Quadrilaterals\u003c\/p\u003e \u003cp\u003eAngles Inscribed in Circles\u003c\/p\u003e \u003cp\u003eRules of Logic\u003c\/p\u003e \u003cp\u003e1.3 Exercises\u003c\/p\u003e \u003cp\u003e1.4 Chapter Overview\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eTWO  Constructing → Proving\u003c\/p\u003e \u003cp\u003e 2.1 Activities\u003c\/p\u003e \u003cp\u003e 2.2 Discussion: Euclid’s Postulates and Constructions\u003c\/p\u003e \u003cp\u003e Euclid’s Postulates\u003c\/p\u003e \u003cp\u003e Congruence and Similarity\u003c\/p\u003e \u003cp\u003e Constructions\u003c\/p\u003e \u003cp\u003e Geometric Language Revisited\u003c\/p\u003e \u003cp\u003e Conditional Statements: Implication\u003c\/p\u003e \u003cp\u003e Using Robust Constructions to Develop a Proof\u003c\/p\u003e \u003cp\u003e Angles and Measuring Angles\u003c\/p\u003e \u003cp\u003e Constructing Perpendicular and Parallel Lines\u003c\/p\u003e \u003cp\u003e Properties of Triangles\u003c\/p\u003e \u003cp\u003e Euclid’s Parallel Postulate\u003c\/p\u003e \u003cp\u003e Euclid’s Constructions in the Elements\u003c\/p\u003e \u003cp\u003e Ideas About Betweenness\u003c\/p\u003e \u003cp\u003e 2.3 Exercises\u003c\/p\u003e \u003cp\u003e 2.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eTHREE Mathematical Arguments and Triangle Geometry\u003c\/p\u003e \u003cp\u003e3.1 Activities\u003c\/p\u003e \u003cp\u003e3.2 Discussion\u003c\/p\u003e \u003cp\u003eDeductive Reasoning\u003c\/p\u003e \u003cp\u003eUniversal and Existential Quantifiers\u003c\/p\u003e \u003cp\u003eNegating a Quantified Statement\u003c\/p\u003e \u003cp\u003eDirect Proof and Disproof by Counterexample\u003c\/p\u003e \u003cp\u003eStep-by-Step Proofs\u003c\/p\u003e \u003cp\u003eCongruence Criteria for Triangles\u003c\/p\u003e \u003cp\u003eThe Converse and the Contrapositive\u003c\/p\u003e \u003cp\u003eConcurrence Properties for Triangles\u003c\/p\u003e \u003cp\u003eCeva’s Theorem and Its Converse\u003c\/p\u003e \u003cp\u003eBrief Excursion into Circle Geometry\u003c\/p\u003e \u003cp\u003eThe Circumcircle of ΔABC\u003c\/p\u003e \u003cp\u003eThe Nine-Point Circle: A First Pass\u003c\/p\u003e \u003cp\u003eMenelaus’ Theorem and Its Converse\u003c\/p\u003e \u003cp\u003e3.3 Exercises\u003c\/p\u003e \u003cp\u003e3.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eFOUR Circle Geometry and Proofs\u003c\/p\u003e \u003cp\u003e 4.1 Activities\u003c\/p\u003e \u003cp\u003e 4.2 Discussion\u003c\/p\u003e \u003cp\u003e Axiom Systems: Ancient and Modern Approaches\u003c\/p\u003e \u003cp\u003e Language of Circles\u003c\/p\u003e \u003cp\u003e Inscribed Angles\u003c\/p\u003e \u003cp\u003e Mathematical Arguments\u003c\/p\u003e \u003cp\u003e Additional Methods of Proof\u003c\/p\u003e \u003cp\u003e Cyclic Quadrilaterals\u003c\/p\u003e \u003cp\u003e Incircles and Excircles\u003c\/p\u003e \u003cp\u003e Some Interesting Families of Circles\u003c\/p\u003e \u003cp\u003e The Arbelos and the Salinon\u003c\/p\u003e \u003cp\u003e Power of a Point\u003c\/p\u003e \u003cp\u003e The Radical Axis\u003c\/p\u003e \u003cp\u003e The Nine-Point Circle: A Second Pass\u003c\/p\u003e \u003cp\u003e 4.3 Exercises\u003c\/p\u003e \u003cp\u003e 4.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eFIVE Analytic Geometry\u003c\/p\u003e \u003cp\u003e 5.1 Activities\u003c\/p\u003e \u003cp\u003e 5.2 Discussion\u003c\/p\u003e \u003cp\u003e Points\u003c\/p\u003e \u003cp\u003e Lines\u003c\/p\u003e \u003cp\u003e Distance\u003c\/p\u003e \u003cp\u003e Using Coordinates in Proofs\u003c\/p\u003e \u003cp\u003e Another Look at the Radical Axis\u003c\/p\u003e \u003cp\u003e Polar Coordinates\u003c\/p\u003e \u003cp\u003e The Nine-Point Circle, Revisited\u003c\/p\u003e \u003cp\u003e 5.3 Exercises\u003c\/p\u003e \u003cp\u003e 5.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eSIX Taxicab Geometry\u003c\/p\u003e \u003cp\u003e  6.1 Activities\u003c\/p\u003e \u003cp\u003e  6.2 Discussion\u003c\/p\u003e \u003cp\u003e  An Axiom System for Metric Geometry\u003c\/p\u003e \u003cp\u003e  Circles\u003c\/p\u003e \u003cp\u003e  Ellipses\u003c\/p\u003e \u003cp\u003e  Measuring Distance from a Point to a Line\u003c\/p\u003e \u003cp\u003e  Parabolas\u003c\/p\u003e \u003cp\u003e  Hyperbolas\u003c\/p\u003e \u003cp\u003e  Axiom Systems\u003c\/p\u003e \u003cp\u003e  6.3 Exercises\u003c\/p\u003e \u003cp\u003e  6.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eSEVEN  Finite Geometries\u003c\/p\u003e \u003cp\u003e7.1 Activities\u003c\/p\u003e \u003cp\u003e7.2 Discussion\u003c\/p\u003e \u003cp\u003eAn Axiom System for an Affine Plane\u003c\/p\u003e \u003cp\u003eAn Axiom System for a Projective Plane\u003c\/p\u003e \u003cp\u003eDuality\u003c\/p\u003e \u003cp\u003eRelating Affine Planes to Projective Planes\u003c\/p\u003e \u003cp\u003eCoordinates for Finite Geometries\u003c\/p\u003e \u003cp\u003e7.3 Exercises\u003c\/p\u003e \u003cp\u003e7.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eEIGHTTransformational Geometry\u003c\/p\u003e \u003cp\u003e 8.1 Activities\u003c\/p\u003e \u003cp\u003e 8.2 Discussion\u003c\/p\u003e \u003cp\u003e Transformations\u003c\/p\u003e \u003cp\u003e Isometries\u003c\/p\u003e \u003cp\u003e Other Transformations\u003c\/p\u003e \u003cp\u003e Composition of Isometries\u003c\/p\u003e \u003cp\u003e Inverse Isometries\u003c\/p\u003e \u003cp\u003e Using Isometries in Proofs\u003c\/p\u003e \u003cp\u003e Isometries in Space\u003c\/p\u003e \u003cp\u003e8.3 Exercises\u003c\/p\u003e \u003cp\u003e8.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eNINE  Isometries and Matrices\u003c\/p\u003e \u003cp\u003e9.1 Activities\u003c\/p\u003e \u003cp\u003e9.2 Discussion\u003c\/p\u003e \u003cp\u003e Using Vectors to Represent Translations\u003c\/p\u003e \u003cp\u003e Using Matrices to Represent Rotations\u003c\/p\u003e \u003cp\u003e Using Matrices to Represent Reflections\u003c\/p\u003e \u003cp\u003e Composition of Isometries\u003c\/p\u003e \u003cp\u003e The General Form of a Matrix Representation\u003c\/p\u003e \u003cp\u003e Using Matrices in Proofs\u003c\/p\u003e \u003cp\u003e Similarity Transformations\u003c\/p\u003e \u003cp\u003e 9.3 Exercises\u003c\/p\u003e \u003cp\u003e 9.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eTENSymmetry in the Plane\u003c\/p\u003e \u003cp\u003e 10.1 Activities\u003c\/p\u003e \u003cp\u003e 10.2 Discussion\u003c\/p\u003e \u003cp\u003e Symmetries\u003c\/p\u003e \u003cp\u003e Groups of Symmetries\u003c\/p\u003e \u003cp\u003e Classifying Figures by Their Symmetries\u003c\/p\u003e \u003cp\u003e Friezes and Symmetry\u003c\/p\u003e \u003cp\u003e Wallpaper Symmetry\u003c\/p\u003e \u003cp\u003e Tilings\u003c\/p\u003e \u003cp\u003e 10.3 Exercises\u003c\/p\u003e \u003cp\u003e 10.4 Chapter Overview\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eELEVEN  Hyperbolic Geometry\u003c\/p\u003e \u003cp\u003e Part I: Exploring a New Universe\u003c\/p\u003e \u003cp\u003e 11.1 Activities Part I\u003c\/p\u003e \u003cp\u003e 11.2 Discussion Part I\u003c\/p\u003e \u003cp\u003e  Hyperbolic Lines and Segments\u003c\/p\u003e \u003cp\u003e  The Poincaré Disk Model of the Hyperbolic Plane\u003c\/p\u003e \u003cp\u003e  Measuring Distance in the Poincaré Disk Model\u003c\/p\u003e \u003cp\u003e  Hyperbolic Circles\u003c\/p\u003e \u003cp\u003e  Hyperbolic Triangles\u003c\/p\u003e \u003cp\u003e  Circumcircles and Incircles of Hyperbolic Triangles\u003c\/p\u003e \u003cp\u003e  Congruence of Triangles in the Hyperbolic Plane\u003c\/p\u003e \u003cp\u003e Part II: The Parallel Postulate in Hyperbolic Geometry\u003c\/p\u003e \u003cp\u003e 11.3 Activities Part II\u003c\/p\u003e \u003cp\u003e 11.4 Discussion Part II\u003c\/p\u003e \u003cp\u003e  The Hyperbolic and Elliptic Parallel Postulates\u003c\/p\u003e \u003cp\u003e  The Angle of Parallelism\u003c\/p\u003e \u003cp\u003e  The Exterior Angle Theorem\u003c\/p\u003e \u003cp\u003e  Quadrilaterals in the Hyperbolic Plane\u003c\/p\u003e \u003cp\u003e  Another Look at Triangles in the Hyperbolic Plane\u003c\/p\u003e \u003cp\u003e Area in the Hyperbolic Plane\u003c\/p\u003e \u003cp\u003e 11.5 Exercises\u003c\/p\u003e \u003cp\u003e  The Upper-Half-Plane Model\u003c\/p\u003e \u003cp\u003e 11.6 Chapter Overview\u003c\/p\u003e \u003cp\u003eTWELVE Projective Geometry\u003c\/p\u003e \u003cp\u003e12.1 Activities\u003c\/p\u003e \u003cp\u003e12.2 Discussion\u003c\/p\u003e \u003cp\u003e  An Axiom System\u003c\/p\u003e \u003cp\u003e  Models for the Projective Plane\u003c\/p\u003e \u003cp\u003e  Duality\u003c\/p\u003e \u003cp\u003e  Coordinates for Projective Geometry\u003c\/p\u003e \u003cp\u003e  Projective Transformations\u003c\/p\u003e \u003cp\u003e12.3 Exercises\u003c\/p\u003e \u003cp\u003e12.4 Chapter Overview\u003c\/p\u003e \u003cp\u003eAPPENDIX A Trigonometry\u003c\/p\u003e \u003cp\u003eA.1 Activities\u003c\/p\u003e \u003cp\u003eA.2 Discussion\u003c\/p\u003e \u003cp\u003e  Right Triangle Trigonometry\u003c\/p\u003e \u003cp\u003e  Unit Circle Trigonometry\u003c\/p\u003e \u003cp\u003e  Solving Trigonometric Equations\u003c\/p\u003e \u003cp\u003e  Double Angle Formulas\u003c\/p\u003e \u003cp\u003e Angle Sum Formulas\u003c\/p\u003e \u003cp\u003e Half-Angle Formulas\u003c\/p\u003e \u003cp\u003e The Law of Sines and the Law of Cosines\u003c\/p\u003e \u003cp\u003eA.3 Exercises\u003c\/p\u003e \u003cp\u003eAPPENDIX B Calculating with Matrices\u003c\/p\u003e \u003cp\u003eB.1 Activities\u003c\/p\u003e \u003cp\u003eB.2 Discussion\u003c\/p\u003e \u003cp\u003e  Linear Combinations of Vectors\u003c\/p\u003e \u003cp\u003e  Dot Product of Vectors\u003c\/p\u003e \u003cp\u003e  Multiplying a Matrix Times a Vector\u003c\/p\u003e \u003cp\u003e  Multiplying Two Matrices\u003c\/p\u003e \u003cp\u003e The Determinant of a Matrix\u003c\/p\u003e \u003cp\u003eB.3 Exercises\u003c\/p\u003e \u003cp\u003eBIBLIOGRAPHY\u003c\/p\u003e \u003cp\u003eINDEX\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988945780965,"sku":"NP9781119718116","price":145.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119718116.jpg?v=1761782158","url":"https:\/\/k12savings.com\/products\/college-geometry-with-geogebra-isbn-9781119718116","provider":"K12savings","version":"1.0","type":"link"}