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 The presentation is concise and practical; some of the theorem and proof rigor of a traditional geometry course has been replaced by a more intuitive approach that emphasizes applications to future coursework and to everyday life.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.
(A Review and a Test conclude each chapter.)
1. Foundations of Geometry.
Logical Systems. 2. Introduction to Proof.
Points, Lines, and Planes.
Segments, Rays, and Angles.
Direct Proofs. 3. Triangles.
Proofs Involving Lines and Angles.
Constructions Involving Lines and Angles.
Classifying Triangles. 4. Parallel Lines and Polygons.
Proofs Involving Congruence.
Isosceles Triangles, Medians, and Altitudes.
Constructions Involving Triangles.
Indirect Proof and the Parallel Postulate. 5. Ratio, Proportion, and Similarity.
Transversals and Angles.
Polygons and Angles.
Parallelograms and Rhombuses.
Rectangles, Squares, and Trapezoids.
Areas of Polygons.
Ratio and Proportion. 6. Right Triangles and the Pythagorean Theorem.
More Theorems on Similar Triangles.
Review of Radicals and Quadratic Equations (Optional). 7. Circles.
Properties of Right Triangles.
The Pythagorean Theorem.
Circles and Arcs. 8. Inequalities.
Chords and Secants.
Circles and Regular Polygons.
Sectors, Arc Length, and Area.
Inequalities. 9. Solid Geometry.
Inequalities Involving Circles.
Planes and the Polyhedron. 10. Geometric Loci.
Prisms and Pyramids.
Cylinders and Cones.
Spheres and Composite Features.
Locus and Basic Theorems. 11. Introduction to Analytic Geometry.
Triangle Concurrency Theorems.
The Cartesian Coordinate System. 12. Triangle Trigonometry.
Slope, Distance, and Midpoint Formulas.
Proofs Involving Polygons.
The Trigonometric Ratios.
Solving Right Triangles.
Applications Involving Right Triangles.
Postulates of Geometry.
Theorems and Corollaries of Geometry.
Constructions in Geometry.