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This applications-oriented text covers all the geometry needed by students planning to take courses in intermediate algebra, college algebra, trigonometry, or calculus. It presumes an understanding of beginning algebra. The presentation is concise and practical; some of the theorem and proof rigor of a traditional geometry course has been replaced by a more intuitive approach that emphasizes applications to future coursework and to everyday life. Essentials of Geometry for College Students features the accessible writing style and thorough pedagogy that have distinguished the many successful texts by the authors. Full-page chapter introductions, with striking photographs, preview applications that are solved later in the chapter. Throughout, detailed examples with step-by-step solutions and second-color annotations ensure comprehension. Definitions, postulates, theorems, and constructions are set off in colored boxes. Practice exercises parallel examples to help students assimilate concepts and techniques. An extensive exercise set follows each section, offering both routine drill problems and more challenging applications and extensions. Historical background, brainteasers, and illustrations to add interest.
Table of Contents
(A Review and a Test conclude each chapter.) 1. Foundations of Geometry.
Logical Systems. Points, Lines, and Planes. Segments, Rays, and Angles.
2. Introduction to Proof.
Direct Proofs. Proofs Involving Lines and Angles. Constructions Involving Lines and Angles.
Indirect Proof and the Parallel Postulate. Transversals and Angles. Polygons and Angles. Parallelograms and Rhombuses. Rectangles, Squares, and Trapezoids. Areas of Polygons.
5. Ratio, Proportion, and Similarity.
Ratio and Proportion. Similar Polygons. More Theorems on Similar Triangles.
6. Right Triangles and the Pythagorean Theorem.
Review of Radicals and Quadratic Equations (Optional). Properties of Right Triangles. The Pythagorean Theorem.
7. Circles.
Circles and Arcs. Chords and Secants. Tangents. Circles and Regular Polygons. Sectors, Arc Length, and Area.
Planes and the Polyhedron. Prisms and Pyramids. Cylinders and Cones. Spheres and Composite Features.
10. Geometric Loci.
Locus and Basic Theorems. Triangle Concurrency Theorems.
11. Introduction to Analytic Geometry.
The Cartesian Coordinate System. Slope, Distance, and Midpoint Formulas. Circles. Proofs Involving Polygons.
12. Triangle Trigonometry.
The Trigonometric Ratios. Solving Right Triangles. Applications Involving Right Triangles. Appendixes. Postulates of Geometry. Theorems and Corollaries of Geometry. Constructions in Geometry.