Cover image for Geometry

Geometry

Author Rebecca Dayton , Sonal Bhatt
Release Date: 2014/07/01
ISBN: 9781615645008
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Book Description

Just about everyone takes a geometry class at one time or another. And while some people quickly grasp the concepts, most find geometry challenging. Covering everything one would expect to encounter in a high school or college course, Idiot's Guides: Geometry covers everything a student would need to know. This all-new book will integrate workbook-like practice questions to reinforce the lessons. In addition, a glossary of terms, postulates, and theorems provide a quick reference to need-to-know information as well. Easy-to-understand, step-by-step explanations walk the reader through:

- Basics of Geometry
- Reasoning and Proof
- Perpendicular and Parallel Lines
- Congruent Triangles
- Properties of Triangles
- Quadrilaterals
- Transformations
- Similarity
- Right Triangles and Trigonometry
- Circles
- Area of Polygons and Circles
- Surface Area and Volume

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Introduction
  5. Part 1: The Foundations of Geometry
    1. 1 The Basics of Geometry
      1. Basic Terminology
        1. Points, Lines, and Planes
        2. Segments and Rays
      2. Identifying Parts of Geometric Figures
      3. Relationships Between Lines and Planes
      4. Point, Line, and Plane Postulates
    2. 2 Angles
      1. An Introduction to Angles
      2. Types of Angles
      3. How to Measure Angles
      4. Angle Relationships
        1. Complementary and Supplementary Angles
        2. Adjacent and Vertical Angles
        3. Using Angle Relationships to Solve Equations
    3. 3 Segment and Angle Addition
      1. Segment Addition
        1. Numerical Examples
        2. Algebraic Examples
      2. Angle Addition
        1. Numerical Examples
        2. Algebraic Examples
    4. 4 Introduction to Coordinate Geometry
      1. Coordinate Planes
      2. Finding the Distance Between Two Points
      3. Midpoint
      4. Linear Relationships
        1. Proving Lines Are Parallel
        2. Proving Lines Are Perpendicular
  6. Part 2: Reasoning and Proof
    1. 5 Inductive vs. Deductive Reasoning
      1. Inductive Reasoning
      2. Conditional Statements
        1. Parts of a Conditional Statement
        2. Verifying the Validity of Conditional Statements
      3. Related Conditionals
        1. Converses and Biconditionals
        2. Negations
        3. Drawing Conclusions Using Related Conditionals
      4. Deductive Reasoning
    2. 6 Creating Two-Column Proofs
      1. Developing a Proof
      2. Algebraic Proofs
      3. Geometric Proofs
        1. Proofs Involving Segments
        2. Proofs Involving Angles
    3. 7 Parallel and Perpendicular Lines
      1. Parallel Lines in Relation to Angles
        1. Using Parallel Angle Pair Relationships to Solve Problems
        2. Proving Lines Are Parallel
      2. Perpendicular Lines in Relation to Angles
        1. Using Perpendicular Line Theorems to Solve Problems
        2. Proving Lines Are Perpendicular
  7. Part 3: Triangles
    1. 8 Introducing Triangles
      1. Triangle Classifications
      2. Concurrent Lines and Segments Related to Triangles
        1. Altitudes
        2. Medians
        3. Angle Bisectors
        4. Perpendicular Bisectors
      3. Midsegments
      4. Proportional Segments
      5. Inequality Theorems
        1. Triangle Inequality Theorem
        2. Side Angle Inequality Theorem
        3. Exterior Angle Inequality Theorem
        4. Hinge Theorem
    2. 9 Right Triangles and Trigonometry
      1. The Pythagorean Theorem
        1. Pythagorean Triples
        2. The Converse of the Pythagorean Theorem
      2. Altitude Drawn to the Hypotenuse
      3. Special Right Triangles
        1. 30°-60°-90° Triangle
        2. 45°-45°-90° Triangle
      4. Trigonometric Ratios
    3. 10 Congruent Triangles
      1. Corresponding Sides and Angles of Two Triangles
      2. Postulates and Theorems for Congruent Triangles
      3. Proving Triangles Are Congruent
      4. Proving Corresponding Parts of Congruent Triangles Are Congruent
  8. Part 4 Two-Dimensional Figures
    1. 11 Polygons
      1. Classifying Polygons
        1. Characteristics of Polygons
        2. Polygons with n Sides
        3. Regular Polygons
        4. Convex vs. Concave
      2. Angle Measures of Polygons
        1. The Sum of the Interior Angles of a Convex Polygon
        2. The Sum of the Exterior Angles of a Convex Polygon
      3. Perimeter and Area of Polygons
        1. Perimeter
        2. Area
    2. 12 Special Quadrilaterals
      1. The Family of Special Quadrilaterals
      2. Parallelograms
        1. Parallelograms in Detail
        2. Parallelogram Measurement Equations
        3. Parallelogram Dimension Equations
      3. Trapezoids
        1. Trapezoids in Detail
        2. Trapezoid Measurement Equations
      4. Kites
        1. Kites in Detail
        2. Kite Measurement Equations
      5. Proving Parallelograms
        1. Parallelograms on a Coordinate Grid
        2. Parallelogram Two-Column Proofs
      6. Proving Trapezoids and Kites
        1. Using Properties of Trapezoids
        2. Using Properties of Kites
    3. 13 Similar Figures
      1. Ratios and Proportions
      2. Similar Polygons
      3. A Numerical Example
      4. An Algebraic Example
      5. Similar Polygons on a Coordinate Plane
      6. Proportions with Area
      7. Applications of Similar Triangles
      8. Indirect Measurement
      9. Overlapping Triangles
      10. Proving Triangles Are Similar
      11. AA Similarity Theorem
      12. SSS Similarity Theorem
      13. SAS Similarity Theorem
  9. Part 5: Three-Dimensional Figures
    1. 14 Solid Geometry
      1. Solid Figures
        1. Polyhedrons
        2. Nonpolyhedrons
      2. Nets
      3. Euler’s Formula
    2. 15 Measuring Solid Figures
      1. Surface Area
        1. The Surface Area of Prisms and Cylinders
        2. The Surface Area of Pyramids and Cones
      2. Volume
        1. The Volume of Prisms and Cylinders
        2. The Volume of Pyramids and Cones
      3. Spheres
        1. Surface Area
        2. Volume
      4. Similar Solids
      5. The Effect of Dilation on Surface Area and Volume
  10. Part 6: Circles
    1. 16 Properties of Circles
      1. Lines and Segments Related to Circles
      2. Properties of Tangents
      3. Arcs and Angles
        1. Central Angles and Inscribed Angles
        2. Types of Arcs
        3. Determining the Measure of an Arc with Angles
      4. Theorems Associated with Chords
        1. Lengths of Intersecting Chords Theorem
        2. Angles Formed by Intersecting Chords Theorem
      5. Angles Formed by Secants and Tangents
    2. 17 Circle Circumference and Area
      1. Circumference of a Circle
      2. Arc Length
      3. Area of a Circle
      4. Area of a Sector
      5. Application of Circumference and Area
  11. Part 7: Coordinate Geometry
    1. 18 A Deeper Look at Coordinate Geometry
      1. Conic Sections
      2. Circles
        1. Writing the Equation for a Circle
        2. Using Other Information to Write a Circle Equation
        3. Graphing a Circle
      3. Parabolas
        1. Writing the Equation for a Parabola That Opens Right or Left
        2. Writing the Equation for a Parabola That Opens Up or Down
      4. Ellipses
        1. Writing the Equation for an Ellipse with a Horizontal Axis
        2. Writing the Equation for an Ellipse with a Vertical Axis
        3. Using Foci to Find Missing Values
    2. 19 Transformations
      1. Congruence Transformations
        1. Translation
        2. Reflection
        3. Rotation
      2. Composite Transformations
        1. Glide Reflection
        2. Two Reflections
  12. Part 8: Practice Problems
  13. Appendixes
    1. A Glossary
    2. B Practice Problem Answer Key
  14. Index
3.147.54.6