Barron’s Math 360: A Complete Study Guide to Geometry with Online Practice

Cover
Title Page
Copyright
Contents
How to Use This Book
1. Building a Geometry Vocabulary
    The Building Blocks of Geometry
    Definitions and Postulates
    Inductive Versus Deductive Reasoning
    The IF … THEN … Sentence Structure
    Review Exercises
2. Measure and Congruence
    Measurements of Segments and Angles
    Betweenness of Points and Rays
    Congruence
    Basic Constructions
    Midpoint and Bisector
    Diagrams and Drawing Conclusions
    Properties of Equality and Congruence
    Additional Properties of Equality
    The Two-Column Proof Format
    Review Exercises
3. Angle Pairs and Perpendicular Lines
    Supplementary and Complementary Angle Pairs
    Adjacent and Vertical Angle Pairs
    Theorems Relating to Complementary, Supplementary, and Vertical Angles
    Definitions and Theorems Relating to Right Angles and Perpendiculars
    A Word About the Format of a Proof
    Review Exercises
4. Parallel Lines
    Planes and Lines
    Properties of Parallel Lines
    Converses and Methods of Proving Lines Parallel
    The Parallel Postulate
    Review Exercises
5. Angles of a Polygon
    The Anatomy of a Polygon
    Angles of a Triangle
    Exterior Angles of a Triangle
    Angles of a Polygon
    Review Exercises
6. Proving Triangles Are Congruent
    Correspondences and Congruent Triangles
    Proving Triangles Congruent: SSS, SAS, and ASA Postulates
    Proving Overlapping Triangles Congruent
    Proving Triangles Congruent: AAS and Hy-Leg Methods
    When Two Triangles Are NOT Congruent
    Review Exercises
7. Applying Congruent Triangles
    Using Congruent Triangles to Prove Segments and Angles Congruent
    Using Congruent Triangles to Prove Special Properties of Lines
    Classifying Triangles and Special Segments
    The Isosceles Triangle
    Double Congruence Proofs
    Review Exercises
    Cumulative Review Exercises: Chapters 1–7
8. Transformation Geometry
    Terms and Notation
    Congruence Transformations
    Classifying Isometries
    Size Transformations
    Types of Symmetry
    Transformations in the Coordinate Plane
    Composing Transformations
    Congruent Proofs Using Transformations
    Review Exercises
9. Ratio, Proportion, and Similarity
    Ratio and Proportion
    Proportions in a Triangle
    When Are Polygons Similar?
    Proving Triangles Similar
    Proving Lengths of Sides of Similar Triangles in Proportion
    Proving Products of Segment Lengths Equal
    Applications of Similar Triangles
    Review Exercises
10. The Right Triangle
    Proportions in a Right Triangle
    The Pythagorean Theorem
    Special Right-Triangle Relationships
    Trigonometric Ratios
    Indirect Measurement in a Right Triangle
    Review Exercises
11. Geometric Inequalities, Indirect Proof, and Concurrencies
    Some Basic Properties of Inequalities
    Inequality Relationships in a Triangle
    Points of Concurrency in a Triangle
    The Indirect Method of Proof
    Review Exercises
    Cumulative Review Exercises: Chapters 8–11
12. Special Quadrilaterals
    Classifying Quadrilaterals
    Properties of a Trapezoid
    Properties of a Parallelogram
    Properties of Special Parallelograms
    Proving a Quadrilateral Is a Parallelogram
    The Isosceles Trapezoid
    Review Exercises
13. Circles and Angle Measurement
    The Parts of a Circle
    Arcs and Central Angles
    Diameters and Chords
    Tangents and Secants
    Angle Measurement: Vertex on the Circle
    Angle Measurement: Vertex in the Interior of the Circle
    Angle Measurement: Vertex in the Exterior of the Circle
    Using Angle-Measurement Theorems
    Review Exercises
14. Chord, Tangent, and Secant Segments
    Equidistant Chords
    Tangents and Circles
    Similar Triangles and Circles
    Tangent- and Secant-Segment Relationships
    Circumference and Arc Length
    Review Exercises
15. Area and Volume
    Areas of a Rectangle, Square, and Parallelogram
    Area of a Triangle
    Comparing Areas
    Areas of a Circle, Sector, and Segment
    Geometric Solids
    Similar Solids
    Review Exercises
16. Coordinate Geometry
    Finding Area Using Coordinates
    The Midpoint and Distance Formulas
    Partitioning a Line Segment
    Slope of a Line
    Equation of a Line
    Equation of a Circle
    Proofs Using Coordinates
    Review Exercises
    Cumulative Review Exercises: Chapters 12–16
Some Geometric Relationships and Formulas Worth Remembering
Glossary
Answers to Chapter Review Exercises
Solutions to Cumulative Review Exercises