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Book

Geometry : includes plane, analytic, and transformational geometries

Call Number

  • 516 R498 (CEN)

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Edition

4th ed.

Publication Information

New York : McGraw Hill, c2009.

Physical Description

x, 326 p. : ill. ; 28 cm.

Summary

665 fully solved problems; concise explanations of all geometry concepts; covers solid geometry and transformation.

Notes

Includes index.

Contents

  • ch . 1. Lines, angles, and triangles
  • 1.1. Historical background of geometry
  • 1.2. Undefined terms of geometry : point, line, and plane
  • 1.3. Line segments
  • 1.4. Circles
  • 1.5. Angles
  • 1.6. Triangles
  • 1.7. Pairs of angles
  • ch. 2. Methods of proof
  • 2.1. Proof by deductive reasoning
  • 2.2. Postulates (assumptions)
  • 2.3. Basic angle theorems
  • 2.4. Determining the hypothesis and conclusion
  • 2.5. Proving a theorem
  • ch. 3. Congruent triangles
  • 3.1. Congruent triangles
  • 3.2. Isosceles and equilateral triangles
  • ch. 4. Parallel lines, distances, and angle sums
  • 4.1. parallel lines
  • 4.2. Distances
  • 4.3. Sum of the measures of the angles of a triangle
  • 4.4. Sum of the measures of the angles of a polygon
  • 4.5. Two new congruency theorems
  • ch. 5. Parallelograms, trapezoids, medians, and midpoints
  • 5.1. Trapezoids
  • 5.2. Parallelograms
  • 5.3. Special parallelograms : rectangle, rhombus, and square
  • 5.4. Three or more parallels ; medians and midpoints
  • ch. 6. Circles
  • 6.1. The circle ; circle relationships
  • 6.2. Tangents
  • 6.3. Measurement of angles and arcs in a circle
  • ch. 7. Similarity
  • 7.1. Ratios
  • 7.2. Proportions
  • 7.3. Proportional segments
  • 7.4. Similar triangles
  • 7.8. Mean proportionals in a right triangle
  • 7.9. Pythagorean theorem
  • 7.10. Special right triangles
  • ch. 8. Trigonometry
  • 8.1. Trigonometric ratios
  • 8.2. Angles of elevation and depression
  • ch. 9. Areas
  • 9.1. Area of a rectangle and of a square
  • 9.2. Area of a parallelogram
  • 9.3. Area of a triangle
  • 9.4. Area of a trapezoid
  • 9.5. Area of a rhombus
  • 9.6. Polygons of the same size or shape
  • 9.7. Comparing areas of similar polygons
  • ch. 10. Regular polygons and the circle
  • 10.1. Regular polygons
  • 10.2. Relationships of segments in regular polygons of 3, 4, and 6 sides
  • 10.3. Area of a regular polygon
  • 10.4. Ratios of segments and areas of regular polygons
  • 10.5. Circumference and area of a circle
  • 10.6. Length of an arc ; area of a sector and a segment
  • 10.7. Areas of combination figures
  • ch. 11. Locus
  • 11.1. Determining a locus
  • 11.2. Locating points by means of intersecting loci
  • 11.3. Proving a locus
  • ch. 12. Analytic geometry
  • 12.1. Graphs
  • 12.2. Midpoint of a segment
  • 12.3. Distance between two points
  • 12.4. Slope of a line
  • 12.5. Locus in analytic geometry
  • 12.6. Areas in analytic geometry
  • 12.7. Proving theorems with analytic geometry
  • ch. 13. Inequalities and indirect reasoning
  • 13.1. Inequalities
  • 13.2. Indirect reasoning
  • ch. 14. Improvement of reasoning
  • 14.1. Definitions
  • 14.2. Deductive reasoning in geometry
  • 14.3. Converse, inverse, and contrapositive of a statement
  • 14.4. Partial converse and partial inverse of a theorem
  • 14.5. Necessary and sufficient conditions
  • ch. 15. Constructions
  • 15.1. Introduction
  • 15.2. Duplicating segments and angles
  • 15.3. Constructing bisectors and perpendiculars
  • 15.4. Constructing a triangle
  • 15.5. Constructing parallel lines
  • 15.6. Circle constructions
  • 15.7. Inscribing and circumscribing regular polygons
  • 15.8. Constructing similar triangles
  • ch. 16. Proofs of important theorems
  • 16.1. Introduction
  • 16.2. The proofs
  • ch. 17. Extending plane geometry into solid geometry
  • 17.1. Solids
  • 17.2. Extensions to solid geometry
  • 17.3. Areas of solids : square measure
  • 17.4. Volumes of solids : cubic measure
  • ch. 18. Transformations
  • 18.1. Introduction to transformations
  • 18.2. Transformation notation
  • 18.3. Translations
  • 18.4. Reflections
  • 18.5. Rotations
  • 18.6. Rigid motions
  • 18.7. Dihilations
  • ch. 19. Non-Euclidean geometry
  • 19.1. The foundations of geometry
  • 19.2. The postulates of Euclidean geometry
  • 19.3. The fifth postulate problem
  • 19.4. Different geometries
  • Formulas for references
  • Answers to supplementary problems
  • Index.

Subjects

Added Authors

Christopher Thomas