Solution Manual for Foundations of Geometry, 2/E 2nd Edition Gerard Venema

Solution Manual for Foundations of Geometry, 2/E 2nd Edition Gerard Venema digital download immediately after payment is complete.

Product details:

• ISBN-10 ‏ : ‎ 0136020585
• ISBN-13 ‏ : ‎ 978-0136020585
• Author: Gerard Venema

Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers―and encourages students to make connections between their college courses and classes they will later teach. This text’s coverage begins with Euclid’s Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra.

Table Of Contents:

1. Prologue: Euclid’s Elements

1.1 Geometry before Euclid

1.2 The logical structure of Euclid’s Elements

1.3 The historical significance of Euclid’s Elements

1.4 A look at Book I of the Elements

1.5 A critique of Euclid’s Elements

1.6 Final observations about the Elements

2. Axiomatic Systems and Incidence Geometry

2.1 The structure of an axiomatic system

2.2 An example: Incidence geometry

2.3 The parallel postulates in incidence geometry

2.4 Axiomatic systems and the real world

2.5 Theorems, proofs, and logic

2.6 Some theorems from incidence geometry

3. Axioms for Plane Geometry

3.1 The undefined terms and two fundamental axioms

3.2 Distance and the Ruler Postulate

3.3 Plane separation

3.4 Angle measure and the Protractor Postulate

3.5 The Crossbar Theorem and the Linear Pair Theorem

3.6 The Side-Angle-Side Postulate

3.7 The parallel postulates and models

4. Neutral Geometry

4.1 The Exterior Angle Theorem and perpendiculars

4.2 Triangle congruence conditions

4.3 Three inequalities for triangles

4.4 The Alternate Interior Angles Theorem

4.5 The Saccheri-Legendre Theorem

4.6 Quadrilaterals

4.7 Statements equivalent to the Euclidean Parallel Postulate

4.8 Rectangles and defect

4.9 The Universal Hyperbolic Theorem

5. Euclidean Geometry

5.1 Basic theorems of Euclidean geometry

5.2 The Parallel Projection Theorem

5.3 Similar triangles

5.4 The Pythagorean Theorem

5.5 Trigonometry

5.6 Exploring the Euclidean geometry of the triangle

6. Hyperbolic Geometry

6.1 The discovery of hyperbolic geometry

6.2 Basic theorems of hyperbolic geometry

6.3 Common perpendiculars

6.4 Limiting parallel rays and asymptotically parallel lines

6.5 Properties of the critical function

6.6 The defect of a triangle

6.7 Is the real world hyperbolic?

7. Area

…

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