# Schaum's Outline of Geometry, Sixth Edition

by: Barnett Rich, PhD, Christopher Thomas, PhD

**Abstract:**Tough test questions? Missed lectures? Not enough time? Textbook too pricey? Fortunately, there's Schaum's. This all-in-one-package includes hundreds of fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems—it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand. Schaum's Outline of Geometry, Sixth Edition, features: • 665 practice problems with step-by-step solutions • 451 supplementary problems to reinforce knowledge • Concise explanations of all geometry concepts • Guidelines for proofs, a new chapter on conics, and coverage of solid geometry and transformations • Support for all major textbooks for geometry courses • Access to revised Schaums.com website with 25 problem-solving videos, and more

Full details

## Table of Contents

**A.**Preface to the First Edition**B.**Introduction**1.**Lines, Angles, and Triangles**2.**Methods of Proof**3.**Congruent Triangles**4.**Parallel Lines, Distances, and Angle Sums**5.**Parallelograms, Trapezoids, Medians, and Midpoints**6.**Circles**7.**Similarity**8.**Trigonometry**9.**Areas**10.**Regular Polygons and the Circle**11.**Locus**12.**Analytic Geometry**13.**Inequalities and Indirect Reasoning**14.**Improvement of Reasoning**15.**Constructions**16.**Proofs of Important Theorems**17.**Extending Plane Geometry into Solid Geometry**18.**Transformations**19.**Conic Sections**20.**Non-Euclidean Geometry**A.**Formulas for Reference**B.**Answers to Supplementary Problems

## Tools & Media

## Expanded Table of Contents

**A.**Preface to the First Edition**B.**Introduction**1.**Lines, Angles, and Triangles**2.**Methods of Proof**3.**Congruent Triangles**4.**Parallel Lines, Distances, and Angle Sums**5.**Parallelograms, Trapezoids, Medians, and Midpoints**6.**Circles**7.**Similarity- Ratios
- SOLVED PROBLEMS
- Proportions
- SOLVED PROBLEMS
- Proportional Segments
- SOLVED PROBLEMS
- Similar Triangles
- SOLVED PROBLEMS
- Extending A Basic Proportion Principle
- SOLVED PROBLEMS
- Proving Equal Products of Lengths of Segments
- SOLVED PROBLEMS
- Segments Intersecting Inside and Outside a Circle
- SOLVED PROBLEMS
- Mean Proportionals in a Right Triangle
- SOLVED PROBLEMS
- Pythagorean Theorem
- SOLVED PROBLEMS
- Special Right Triangles
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS

**8.**Trigonometry**9.**Areas- Area of a Rectangle and of a Square
- SOLVED PROBLEMS
- Area of a Parallelogram
- SOLVED PROBLEMS
- Area of a Triangle
- SOLVED PROBLEMS
- Area of a Trapezoid
- SOLVED PROBLEMS
- Area of a Rhombus
- SOLVED PROBLEMS
- Polygons of the Same Size or Shape
- SOLVED PROBLEMS
- Comparing Areas of Similar Polygons
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS

**10.**Regular Polygons and the Circle- Regular Polygons
- SOLVED PROBLEMS
- Relationships of Segments in Regular Polygons of 3, 4, and 6 Sides
- SOLVED PROBLEMS
- Area of a Regular Polygon
- SOLVED PROBLEMS
- Ratios of Segments and Areas of Regular Polygons
- SOLVED PROBLEMS
- Circumference and Area of a Circle
- SOLVED PROBLEMS
- Length of an Arc; Area of a Sector and a Segment
- SOLVED PROBLEMS
- Areas of Combination Figures
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS

**11.**Locus**12.**Analytic Geometry**13.**Inequalities and Indirect Reasoning**14.**Improvement of Reasoning**15.**Constructions- Introduction
- Duplicating Segments and Angles
- SOLVED PROBLEMS
- Constructing Bisectors and Perpendiculars
- SOLVED PROBLEMS
- Constructing a Triangle
- SOLVED PROBLEMS
- Constructing Parallel Lines
- SOLVED PROBLEMS
- Circle constructions
- SOLVED PROBLEMS
- Inscribing and Circumscribing Regular Polygons
- Constructing Similar Triangles
- SOLVED PROBLEMS
- SUPPLEMENTARY PROBLEMS

**16.**Proofs of Important Theorems**17.**Extending Plane Geometry into Solid Geometry**18.**Transformations**19.**Conic Sections- The Standard Conic Sections
- Ellipses
- SOLVED PROBLEMS: FINDING EQUATIONS OF ELLIPSES
- SOLVED PROBLEMS: SKETCHING ELLIPSES
- Parabolas
- SOLVED PROBLEMS: FINDING EQUATIONS OF PARABOLAS
- SOLVED PROBLEMS: SKETCHING PARABOLAS
- Hyperbolas
- SOLVED PROBLEMS: SKETCHING HYPERBOLAS
- SOLVED PROBLEMS: FINDING EQUATIONS OF HYPERBOLAS
- SUPPLEMENTARY PROBLEMS

**20.**Non-Euclidean Geometry**A.**Formulas for Reference**B.**Answers to Supplementary Problems

**Book Details**

**Title: **Schaum's Outline of Geometry, Sixth Edition

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2018 McGraw-Hill Education

**ISBN: **9781260010572

**Authors:****Barnett Rich, PhD**
held a doctor of philosophy (Ph.D.) degree from Columbia University and a doctor of jurisprudence (J.D.) degree from New York University. He began his professional career at Townsend Harris High School in New York City, and was one of the prominent organizers of the High School of Music and Art, where he served as the Administrative Assistant. Later Dr. Rich taught at CUNY and Columbia University and held the post of Chairman of Mathematics at Brooklyn Technical High School for 14 years. Among his many achievements were the 6 degrees that he earned and the 23 books that he wrote, among them Schaum's Outlines of Elementary Algebra and Modern Elementary Algebra and Review of Elementary Algebra.
**Christopher Thomas, PhD**
has a B.S. from the University of Massachusetts at Amherst and a Ph.D. from Tufts University, both in mathematics. He first taught as a Peace Corps volunteer at the Mozano Senior Secondary School in Ghana. Since then he has taught at Tufts University, Texas A&M University, and the Massachusetts College of Liberal Arts. Dr. Thomas has written Schaum's Outline of Math for the Liberal Arts as well as other books on calculus and trigonometry.

**Description: **
Tough test questions? Missed lectures? Not enough time? Textbook too pricey?
Fortunately, there's Schaum's. This all-in-one-package includes hundreds of fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems—it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.
More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.
Schaum's Outline of Geometry, Sixth Edition, features:
• 665 practice problems with step-by-step solutions
• 451 supplementary problems to reinforce knowledge
• Concise explanations of all geometry concepts
• Guidelines for proofs, a new chapter on conics, and coverage of solid geometry and transformations
• Support for all major textbooks for geometry courses
• Access to revised Schaums.com website with 25 problem-solving videos, and more