(Ebook PDF) Elementary Geometry for College Students 7th Edition by Daniel Alexander 9798214342207 full chapters

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ISBN-13 :  9798214342207

Author:  Daniel Alexander 

ELEMENTARY GEOMETRY FOR COLLEGE STUDENTS, 7th Edition, is designed to help students develop a comprehensive vocabulary of geometry, an intuitive and inductive approach to the development of principles, and strong deductive skills to solve geometry-based real-world applications. Over 150 new exercises provide additional practice in writing proofs. Available with access to WebAssign, an online study tool that helps students master the course concepts.

Elementary Geometry for College Students 7th Table of contents:

1. Line and Angle Relationships
1.1. Early Definitions and Postulates
A Mathematical System
Characteristics of a Good Definition
Initial Postulates
1.1. Exercises
1.2. Angles and Their Relationships
Types of Angles
Classifying Pairs of Angles
Constructions with Angles
1.2. Exercises
1.3. Introduction to Geometric Proof
Sample Proofs
1.3. Exercises
1.4. Relationships: Perpendicular Lines
Relations
Constructions Leading to Perpendicular Lines
1.4. Exercises
1.5. The Formal Proof of a Theorem
The Written Parts of a Formal Proof
Converse of a Statement
1.5. Exercises
Perspective on History: The Development of Geometry
Perspective on Applications: Patterns
Summary
Overview
Review Exercises
Chapter 1 Test
2. Parallel Lines
2.1. The Parallel Postulate and Special Angles
Perpendicular Lines
Parallel Lines
Euclidean Geometry
Parallel Lines and Congruent Angles
Parallel Lines and Supplementary Angles
2.1. Exercises
2.2. Indirect Proof
The Law of Negative Inference (Contraposition)
Indirect Proof
2.2. Exercises
2.3. Proving Lines Parallel
2.3. Exercises
2.4. The Angles of a Triangle
2.4. Exercises
2.5. Convex Polygons
Diagonals of a Polygon
Sum of the Interior Angles of a Polygon
Regular Polygons
Polygrams
2.5. Exercises
2.6. Symmetry and Transformations
Line Symmetry
Point Symmetry
Transformations
2.6. Exercises
Perspective on History: Sketch of Euclid
Perspective on Applications: Non-Euclidean Geometries
Summary
Overview
Review Exercises
Chapter 2 Test
3. Triangles
3.1. Congruent Triangles
SSS (Method for Proving Triangles Congruent)
SAS (Method for Proving Triangles Congruent)
Overlapping Triangles
ASA (Method for Proving Triangles Congruent)
AAS (Method for Proving Triangles Congruent)
3.1. Exercises
3.2. Corresponding Parts of Congruent Triangles
Suggestions for Proving Triangles Congruent
Right Triangles
HL (Method for Proving Triangles Congruent)
The Pythagorean Theorem
3.2. Exercises
3.3. Isosceles Triangles
3.3. Exercises
3.4. Basic Constructions Justified
3.4. Exercises
3.5. Inequalities in a Triangle
Lemmas (Helping Theorems)
3.5. Exercises
Perspective on History: Sketch of Archimedes
Perspective on Applications: The Geodesic Dome
Summary
Overview
Review Exercises
Chapter 3 Test
4. Quadrilaterals
4.1. Properties of a Parallelogram
Speed and Direction of Aircraft
4.1. Exercises
4.2. The Parallelogram and Kite
The Parallelogram
The Kite
4.2. Exercises
4.3. The Rectangle, Square, and Rhombus
The Rectangle
The Square
The Rhombus
The Pythagorean Theorem
4.3. Exercises
4.4. The Trapezoid
4.4. Exercises
Perspective on History: Sketch of Thales
Perspective on Applications: Square Number as Sums
Summary
Overview
Review Exercises
Chapter 4 Test
5. Similar Triangles
5.1. Ratios, Rates, and Proportions
5.1. Exercises
5.2. Similar Polygons
5.2. Exercises
5.3. Proving Triangles Similar
5.3. Exercises
5.4. The Pythagorean Theorem
Pythagorean Triples
The Converse of the Pythagorean Theorem
5.4. Exercises
5.5. Special Right Triangles
The 45 ° – 45 ° – 90 ° Right Triangle
The 30 ° – 60 ° – 90 ° Right Triangle
5.5. Exercises
5.6. Segments Divided Proportionally
Ceva’s Theorem
5.6. Exercises
Perspective on History: Proof
Perspective on Applications: Generating Pythagorean Triples
Summary
Overview
Review Exercises
Chapter 5 Test
6. Circles
6.1. Circles and Related Segments and Angles
Angle and Arc Relationships in the Circle
6.1. Exercises
6.2. More Angle Measures in the Circle
6.2. Exercises
6.3. Line and Segment Relationships in the Circle
Circles That Are Tangent
Common Tangent Lines to Circles
Lengths of Line Segments in a Circle
6.3. Exercises
6.4. Some Constructions and Inequalities for the Circle
Constructions of Tangents to Circles
Inequalities in the Circle
6.4. Exercises
Perspective on History: Circumference of the Earth
Perspective on Applications: Sum of Interior Angles of a Polygon
Summary
Overview
Review Exercises
Chapter 6 Test
7. Locus and Concurrence
7.1. Locus of Points
Parabolas
7.1. Exercises
7.2. Concurrence of Lines
7.2. Exercises
7.3. More About Regular Polygons
7.3. Exercises
Perspective on History: The Value of π
Perspective on Applications: The Nine-Point Circle
Summary
Overview
Review Exercises
Chapter 7 Test
8. Areas of Polygons and Circles
8.1. Area and Initial Postulates
Area of a Rectangle
Area of a Parallelogram
Area of a Triangle
8.1. Exercises
8.2. Perimeter and Area of Polygons
Heron’s Formula
Area of a Trapezoid
Quadrilaterals with Perpendicular Diagonals
Area of a Rhombus
Area of a Kite
Areas of Similar Polygons
8.2. Exercises
8.3. Regular Polygons and Area
Area of a Regular Polygon
8.3. Exercises
8.4. Circumference and Area of a Circle
Value of π
Length of an Arc
Limits
Area of a Circle
8.4. Exercises
8.5. More Area Relationships in the Circle
Area of a Sector
Area of a Segment
Area of a Triangle with an Inscribed Circle
8.5. Exercises
Perspective on History: Sketch of Pythagoras
Perspective on Applications: Another Look at the Pythagorean Theorem
Summary
Overview
Review Exercises
Chapter 8 Test
9. Surfaces and Solids
9.1. Prisms, Area, and Volume
Prisms
Area of a Prism
Volume of a Prism
9.1. Exercises
9.2. Pyramids, Area, and Volume
Surface Area of a Pyramid
Volume of a Pyramid
9.2. Exercises
9.3. Cylinders and Cones
Cylinders
Surface Area of a Cylinder
Volume of a Cylinder
Cones
Surface Area of a Cone
Volume of a Cone
Solids of Revolution
9.3. Exercises
9.4. Polyhedrons and Spheres
Polyhedrons
Regular Polyhedrons
Spheres
Surface Area of a Sphere
Volume of a Sphere
9.4. Exercises
Perspective on History: Sketch of René Descartes
Perspective on Applications: Birds in Flight
Summary
Overview
Review Exercises
Chapter 9 Test
10. Analytic Geometry
10.1. The Rectangular Coordinate System
The Distance Formula
The Midpoint Formula
Proof of the Midpoint Formula (Optional)
10.1. Exercises
10.2. Graphs of Linear Equations and Slope
The Graph of an Equation
The Slope of a Line
10.2. Exercises
10.3. Preparing to Do Analytic Proofs
10.3. Exercises
10.4. Analytic Proofs
10.4. Exercises
10.5. Equations of Lines
Slope-Intercept Form of a Line
Point-Slope Form of a Line
Solving Systems of Equations
10.5. Exercises
10.6. The Three-Dimensional Coordinate System
Points
Lines
The Distance Formula
The Midpoint Formula
Planes
Line and Plane Relationships
Intersection of Planes
Spheres
10.6. Exercises
Perspective on History: The Banach-Tarski Paradox
Perspective on Applications: The Point-of-Division Formulas
Summary
Review Exercises
Chapter 10 Test
11. Introduction to Trigonometry
11.1. The Sine Ratio and Applications
11.1. Exercises
11.2. The Cosine Ratio and Applications
11.2. Exercises
11.3. The Tangent Ratio and Other Ratios
11.3. Exercises
11.4. Applications with Acute Triangles
Area of a Triangle
Law of Sines
Law of Cosines
11.4. Exercises
Perspective on History: Sketch of Plato
Perspective on Applications: Radian Measure of Angles
Summary
Review Exercises
Chapter 11 Test
Appendix A. Algebra Review

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