Geometry

Geometry, 1st edition

  • Elayn Martin-Gay

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Overview

Geometry gives you a solid foundation in Euclidean geometry, regardless of your previous experience in geometry. Focused on your success, the author is known for a clear, accessible writing style and for providing innovative resources supporting your mastery of the material.

Published by Pearson (July 14th 2021) - Copyright © 2016

ISBN-13: 9780137554850

Table of contents

1. A Beginning of Geometry
1.1 Tips for Success in Mathematics
1.2 Geometry–A Mathematical System
1.3 Points, Lines, and Planes
1.4 Segments and Their Measure
1.5 Angles and Their Measure
1.6 Angle Pairs and Their Relationships
1.7 Coordinate Geometry–Midpoint and Distance Formulas
1.8 Constructions–Basic Geometry Constructions

2. Introduction to Reasoning and Proofs
2.1 Perimeter, Circumference, and Area
2.2 Patterns and Inductive Reasoning
2.3 Conditional Statements
2.4 Biconditional Statements and Definitions
2.5 Deductive Reasoning
2.6 Reviewing Properties of Equality and Writing Two-Column Proofs
2.7 Proving Theorems About Angles

3. Parallel and Perpendicular Lines
3.1 Lines and Angles
3.2 Proving Lines Are Parallel
3.3 Parallel Lines and Angles Formed by Transversals
3.4 Proving Theorems About Parallel and Perpendicular Lines
3.5 Constructions–Parallel and Perpendicular Lines
3.6 Coordinate Geometry–The Slope of a Line
3.7 Coordinate Geometry–Equations of Lines

4. Triangles and Congruence
4.1 Types of Triangles
4.2 Congruent Figures
4.3 Congruent Triangles by SSS and SAS
4.4 Congruent Triangles by ASA and AAS
4.5 Proofs Using Congruent Triangles
4.6 Isosceles, Equilateral, and Right Triangles

5. Special Properties of Triangles
5.1 Perpendicular and Angle Bisectors
5.2 Bisectors of a Triangle
5.3 Medians and Altitudes of a Triangle
5.4 Midsegments of Triangles
5.5 Indirect Proofs and Inequalities in One Triangle
5.6 Inequalities in Two Triangles

6. Quadrilaterals
6.1 Polygons
6.2 Parallelograms
6.3 Proving that a Quadrilateral Is a Parallelogram
6.4 Rhombuses, Rectangles, and Squares
6.5 Trapezoids and Kites

7. Similarity
7.1 Ratios and Proportions
7.2 Proportion Properties and Problem Solving
7.3 Similar Polygons
7.4 Proving Triangles Are Similar
7.5 Geometric Mean and Similarity in Right Triangles
7.6 Additional Proportions in Triangles

8. Transformations
8.1 Rigid Transformations
8.2 Translations
8.3 Reflections
8.4 Rotations
8.5 Dilations
8.6 Compositions of Reflections
Extension–Frieze Patterns

9. Right Triangles and Trigonometry
9.1 The Pythagorean Theorem and Its Converse
9.2 Special Right Triangles
9.3 Trigonometric Ratios
9.4 Solving Right Triangles
9.5 Vectors
Extension–Law of Sines
Extension–Law of Cosines

10. Area
10.1 Angle Measures of Polygons and Regular Polygon Tessellations
10.2 Areas of Triangles and Quadrilaterals with a Review of Perimeter
10.3 Areas of Regular Polygons
10.4 Perimeters and Areas of Similar Figures
10.5 Arc Measures, Circumferences, and Arc Lengths of Circles
10.6 Areas of Circles and Sectors
10.7 Geometric Probability

11. Surface Area and Volume
11.1 Solids and Cross Sections
11.2 Surface Areas of Prisms and Cylinders
11.3 Surface Areas of Pyramids and Cones
11.4 Volumes of Prisms and Cylinders and Cavalieri's Principle
11.5 Volumes of Pyramids and Cones
11.6 Surface Areas and Volumes of Spheres
11.7 Areas and Volumes of Similar Solids

12. Circles and Other Conic Sections
12.1 Circle Review and Tangent Lines
12.2 Chords and Arcs
12.3 Inscribed Angles
12.4 Additional Angle Measures and Segment Lengths
12.5 Coordinate Plane–Circles
12.6 Locus
Extension–Parabolas

Student Success Resource Section

A Review of Basic Concepts

A.1 Measurement Conversions
A.2 Probability
A.3 Exponents, Order of Operations, and Variable Expressions
A.4 Operations on Real Numbers
A.5 Simplifying Expressions
A.6 Solving Linear Equations
A.7 Solving Linear Inequalities
A.8 Solving Formulas for a Variable
A.9 The Coordinate Plane
A.10 Graphing Linear Equations
A.11 Solving Systems of Linear Equations in Two Variables
A.12 Exponents
A.13 Multiplying Polynomials
A.14 Simplifying Radical Expressions
A.15 Solving Quadratic Equations by Factoring
A.16 Solving Quadratic Equations by the Square Root Property
A.17 Solving Quadratic Equations by the Quadratic Formula

Tables
1. Math Symbols
2. Formulas
3. Measures
4. Properties of Real Numbers

Postulates, Theorems, and Additional Proofs

B. Additional Lessons
B.1 Ellipses and Hyperbolas
B.2 Measurement, Rounding Error, and Reasonableness
B.3 The Effect of Measurement Errors on Calculations

Answers to Selected Exercises
Index
Photo Credits

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