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GeometryMathematics

This book exposes readers to many practical applications of geometry,
especially those involving measurement. A threepart organization divides
topics into Problem Solving, Geometric Shapes, and Measurement; Formal
Synthetic Euclidean Geometry; and Alternate Approaches to Plane Geometry.
Beginning with informal experiences, the book gradually moves toward more
formal proofs, and includes special topics sections.
The authors provide a wealth of pedagogical aids, including over
1,000 exercises, problems, proofs, and applications with answers.
Begins with informal experiences and gradually moves toward more
formal proofs.
Part I, Problem Solving, Geometric Shapes, and Measurement, provides
readers with a fresh start in geometry through problem solving and
applications in measurement.
Part II, Formal Synthetic Euclidean Geometry, contains an extensive,
if somewhat informal, treatment of geometric shapes where initial postulates
and basic course terminology are introduced.
Part III, Alternate Approaches to Plane Geometry, approaches problem
solving/applications in geometry via coordinates and transformations.
Special topics sections at the end of the book cover Real Numbers,
Logic, NonEuclidean Geometry, and Inequalities.
A rich collection of applied problems appears throughout.
Exercises and problems, together with various combinations of proof
and application problems, appear at the end of most sections.
Each section begins with an applied problem whose solution becomes
accessible as the section material unfolds. (A complete solution appears at
the end of the section.)
A "Geometry Around Us" feature appears just before the problem set
at the end of each section.
A wealth of helpful pedagogy includes chapteropening historical
tidbits, "People In Geometry" vignettes, over 1,500 figures, display boxes
highlighting postulates and theorems, paragraph and statementreason proofs,
tips for getting started, and thorough reviews, "Writing for Understanding"
ideas, and practice tests in each chapter along with functional use of color
throughout.
Over 1,000 exercises, problems, proofs, and applications with
answers for odd exercises, problems, and applications provided in the book,
and to even ones provided in the Instructor's Manual.
Most theorems are displayed in three modes: (i) written, (ii)
pictorial, and (iii) symbolic.
I. PROBLEM SOLVING, GEOMETRIC SHAPES, AND MEASUREMENT.
1. Problem Solving in Geometry.
2. Geometric Shapes and Measurement.
3. Perimeter, Area, and Volume.
II. FORMAL SYNTHETIC EUCLIDEAN GEOMETRY.
4. Reasoning and Triangle Congruence.
5. Parallel Lines and Quadrilaterals.
6. Similarity.
7. Circles.
III. ALTERNATE APPROACHES TO PLANE GEOMETRY.
8. Coordinate Geometry.
9. Vector Geometry.
10. Transformation Geometry.
Topic 1. Introduction to Logic.
Topic 2. The Real Number System.
Topic 3. Geometric Inequalities.
Topic 4. NonEuclidean Geometry.
