Revised edition of: Geometry the easy way. 3rd edition 1997

Explains the principles of plane geometry and includes practice exercises and model problems

Preface --

1.

Building a geometry vocabulary -- Building blocks of geometry -- Definitions and postulates -- Inductive versus deductive reasoning -- IF. . . THEN. . . sentence structure -- Review exercises for chapter 1 --

2.

Measure and congruence -- Measuring segments and angles -- Betweenness of points and rays -- Congruence -- Midpoint and bisector -- Diagrams and drawing conclusions -- Properties of equality and congruence -- Additional properties of equality -- Two-column proof format -- Review exercises for chapter 2 --

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 for chapter 3 --

4.

Parallel lines -- Planes and lines -- Properties of parallel lines -- Converses and methods of proving lines parallel -- Parallel postulate -- Review exercises for chapter 4 --

5.

Angles of a polygon -- Anatomy of a polygon -- Angles of a triangle -- Exterior angles of a triangle -- Angles of a polygon -- Review exercises for chapter 5 --

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 for chapter 6 --

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 -- Isosceles triangle -- Double congruence proofs -- Review exercises for chapter 7 -- Cumulative review exercises : chapters 1-7 --

8.

Geometric inequalities -- Some basic properties of inequalities -- Inequality relationships in a triangle -- Indirect method of proof -- Review exercises for chapter 8 --

9.

Special quadrilaterals -- Classifying quadrilaterals -- Properties of a parallelogram -- Properties of special parallelograms -- Proving a quadrilateral is a parallelogram -- Applications of parallelograms -- Properties of a trapezoid -- Review exercises for chapter 9 --

10.

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 -- Review exercises for chapter 10 --

11.

Right triangle -- Proportions in a right triangle -- Pythagorean theorem -- Special right-triangle relationships -- Trigonometric ratios -- Indirect measurement in a right triangle -- Review exercises for chapter 11 -- Cumulative review exercises : chapters 8-11 --

12.

Circles and angle measurement -- 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 for chapter 12 --

13.

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 for chapter 13 --

14.

Area and volume -- Areas of a rectangle, square, and parallelogram -- Areas of a triangle and trapezoid -- Comparing areas -- Area of a regular polygon -- Areas of a circle, sector, and segment -- Geometric solids -- Review exercises for chapter 14 --

15.

Coordinate geometry -- Coordinate plane -- Finding area using coordinates -- Midpoint and distance formulas -- Slope of a line -- Equation of a line -- Equation of a circle -- Proofs using coordinates -- Review exercises for chapter 15 --

16.

Locus and constructions -- Describing points that fit one condition -- Describing points that fit more than one condition -- Locus and coordinates -- Basic constructions -- Review exercises for chapter 16 --

17.

Transformation geometry -- Terms and notation -- Congruence transformations -- Classifying isometries -- Size transformations -- Types of symmetry -- Transformations in the coordinate plane -- Composing Transformations -- Review exercises for chapter 17 -- Cumulative review exercises : chapters 12-17 -- Some geometric relationships and formulas worth remembering -- Glossary -- Answers to chapter exercises -- Solutions to cumulative review exercises