# Best 5 Geometry Textbooks

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Geometry is the study of the relationships between “points, lines, angles, and figures in space”, and the foundation for all of applied mathematics. Geometry is typically a high-school level class and is one of the most anxiety-invoking subjects that students study. This is due to the volume of new concepts introduced and the impact the subject has on subsequent mathematics courses.

No matter your motivation for studying Geometry, it is essential to stick your nose in a quality textbook, in order to ace your class. In this review, we will break down 5 frequently used textbooks: discussing what we liked, what we didn’t, and everything in between.

## 5 Best Geometry Textbooks of all time

### 1. Geometry by Ray C. Jurgensen et al

Moderately priced and popular among teachers who like to put emphasis on learning proofs, Geometry by Ray C. Jurgensen et al., seeks to appeal to the average Geometry student. Unlike some of its counterparts, Geometry focuses on practical application of concepts rather than rote memorization.

Where some of the newer Geometry textbooks flower the pages with multiple graphics, diagrams, and figures, each chapter in Geometry by Jurgensen et al. is concise and straight to the point. Its format is one of this textbook’s strong suits, in that each chapter begins by introducing a theorem and then goes into detail on how to solve it.

The focus of this textbook is teaching the student to reason and solve the Holy Grail of Geometry, two-column proofs. Consequently, Geometry is not recommended for self-study or homeschooled students. This textbook relies heavily on the student-teacher relationship, but could be used as a challenging addition to regular coursework.

Geometry by Jurgensen et al. is a highly-rated, widely-used textbook for teaching the basics of Geometry to the average math student.

#### Pro’s

- Ample examples and detailed explanations of proofs
- Concise and organized information that is easily digestible
- Contains exercises for every level of learner
- More affordable option than its competitors

#### Con’s

- Could be a challenging read for visual learners, as this is not an image-laden textbook
- Requires a teacher for understanding (for most students)
- Lacks visual aids for each concept

### 2. Art of Problem Solving: Introduction to Geometry

Art of Problem Solving: Introduction to Geometry Book Set (2 books) aims to draw upon the fundamentals of mathematics to ensure the student has a solid foundation in geometry basics. This textbook is geared toward instructing grades seven through ten and is a popular textbook among many US high school programs.

The author of The Art of Problem Solving, Richard Rusczyk founded Art of Problem Solving (AoPS) with aspirations to create a space to foster avid math students in their studies and learning. He aims to educate motivated students in all of his endeavors. We can see this theme throughout the book, as there each concept is broken down into digestible segments, with practice problems throughout the lessons. The mathematics language is easily understood by both middle and high schoolers during independent study (Rusczyk, 2006, vii).

The Art of Problem Solving aims not only to teach Geometry to its pupils, but to encourage practical problem solving. Topics are introduced using a discovery approach–a problem is posed for the student to attempt independently. A solution is then provided for clarity. Along the way, theorems are discovered and used to solve the subsequent problems, thus preparing the students for more challenging concepts and problems.

One of the highest rated Geometry textbooks, The Art of Problem Solving, is a great option for learning the fundamentals of Geometry.

#### Pro’s

- This 2-book set can be used for a full stand-alone geometry course.
- Contains over 900 practice problems
- Recommended for students who are interested in STEM fields like engineering, coding, or physics, as well as math competitions
- Format encourages learning and self-study
- One of the only Geometry curriculums to be designed for gifted math student

#### Con’s

- Must purchase both books in the set to get answers and full explanations for all 900 problems
- Material, as well as structure of book, can be considered “over-simplified” to non-beginners

### 3. Elementary Geometry for College Students

Elementary Geometry for College Students was written by Daniel C. Alexander and Geralyn M. Koeberlein with the intent to fill in the gaps left by other leading Geometry textbooks. The authors, both former Geometry teachers themselves, felt most geometry textbooks lacked the “whats, whys, and how tos” needed to be a successful Geometry student (Alexander & Koeberlein, 2020,8). Elementary Geometry for College Students was intended for a high-level learner while still explaining basics on an introductory level.

The structure of the textbook lends itself to be a companion in the Geometry classroom for both teacher and student. The authors introduce a topic “with its relevant vocabulary, examines and explores the concept, develops a number of pertinent theories, verifies the theories deductively, and applies the concept in some real world situations” (Alexander & Koeberlein, 2020, ix).

Complete with visuals, concept reminders, a glossary of terms and formulas, as well as warnings against common pitfalls, this textbook would also be a great resource for self-study and homeschooled students.

#### Pro’s

- Every page has examples and practice problems.
- Focuses on solving proofs as well as explanations and application of each proof
- WebAssign feature accessible by both instructors and students to help pupils further master course concepts (with a focus on learning and writing proofs)
- Lower price point relative to competitors

#### Con’s

- Some technical difficulties reported with both the e-book version and WebAssign feature
- Some equations feature elements that are not defined in the book

### 4. Geometry, Student Edition by McGraw-Hill

Geometry, Student Edition by McGraw-Hill is part of the Common Core math curriculum and is a staple in many high school Geometry courses. It is geared toward grades 9-11, but can be used by anyone studying the subject. The textbook is intended to be a basic introduction into the field of Geometry and was meant to be affordable to the average public school system.

Since Geometry, Student Edition must meet the Common Core State Standards, there are a depth of resources and adaptive technology that aids the teacher in providing instruction to every student. This textbook connects students to the content with print, digital, and interactive resources to prepare the student for end of school year testing (McGraw & Hill, 2012, 13).

Geometry, Student Edition is your run-of-the-mill Geometry textbook, intended for use in a public school system. This textbook has proven effective in preparing students for standardized testing, but is not recommended for those learning the subject on their own, nor for homeschooled students not learning the Common Core curriculum.

#### Pro’s

- Geometry pre-test at the beginning of textbook
- Vocabulary words are defined in both English and Spanish
- Cheapest option on this list
- Digital and interactive resources available supplemental to the textbook
- Teaches to the Common Core standardized test

#### Con’s

- No sequenced index of postulates and theorems
- Lacks the emphasis on application of concepts relative to competitors

### 5. Geometry by Ron Larson et al

Geometry by Ron Larson, Laurie Boswell, and Lee Stiff is designed specifically for grades 9-12 and is the perfect text for self-study. This textbook aims to help the student understand basic principles of Geometry in a clear, concise manner, while still providing an in-depth look into the subject.

Unlike some of this books’ competitors, Geometry explains theorems and proofs in an easily digestible manner and uses repetition to ensure retention of information. This textbook, better than most on the market, uses page breaks and free space in a way that promotes learning and application of the concepts (Larson et al., 2004).

Geometry is a traditional Geometry textbook with ample exercises and in-depth explanations of concepts. While there is little to inspire further exploration into the concepts and principles of geometry, this textbook is recommended for students who are self-studying, as well as, those being homeschooled.

#### Pro’s

- Provides an abundance of examples and practices exercises in every section
- Heavy use of repetition to ensure that students are grasping the information
- Helpful for students planning to take the PAP Geometry exam
- Answer key for all problems in the back of the book

#### Con’s

- Not recommended for students who want a deep dive into proofs and postulates
- Material is dated, compared to current high school curriculum
- Lots of colorful images that are not necessarily relevant to learning the concept
- Disorganized information and omitted topics
- Very heavy (nearly 5 pounds)

Geometry is certainly one of the more difficult subjects to master, as several complex concepts must be learned and perfected. Whether you are self-studying, a homeschooled student, or getting instruction from a classroom, this list has a variety of books that can serve as your GPS to navigate through the world of geometry.

### Frequently Asked Questions

#### Who invented Geometry?

The earliest recorded beginnings of Geometry belong to the people of the ancient Indus Valley and ancient Babylonia with their discovery of the obtuse triangle, around 3000 BC. Ancient Egypt can also be credited with the discovery of early Geometry with the approximations of the area of a circle.

The ancient Greeks and Romans were also major players in breakthroughs of Geometric principles. Great minds like Plato (and his student, Euclid), Thales, and Pythagoras (from Greece) and Archemedes from Italy, paved the way for the modern Geometry that we practice today.

Euclid, however, is often referred to as the “Father of Geometry.” Geometry was developed based on his five postulates. As in, if properties are the cement foundation and theorems are the bricks, then Euclid’s five postulates make up the ground on which the cement is poured and the bricks are laid. Without them there would be no tower of geometry.

#### Why do I have to study Geometry?

As abstract thinking progresses, geometry becomes much more about analysis and reasoning. Throughout high school there is a focus on analyzing properties of two- and three-dimensional shapes, reasoning about geometric relationships, and using the coordinate system. Studying geometry provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, analytical reasoning, and problem-solving.

#### What are the best ways to study for a Geometry test?

First and foremost, diagrams, diagrams, diagrams. Geometry is the study of the relationships between points, lines, surfaces, angles, and shapes. So naturally, drawing diagrams is a must! Understanding the relationships, properties, and theorems will be much easier to understand when you have a visual aid. Don’t rely on your mental math ability to do this. Further, pay attention to the proportions and angles in your drawings. Your diagrams will only help you if they are accurate! Mark down everything in your problem before you start solving the problem. That way, when you are working your way through the problem, you have all the information you need.

Also, know your properties and theorems. These are the bread and butter of geometry and you cannot get very far without them. Make flashcards for all the properties and theorems you need to know and go through them every morning and every night. That way you do not wait until the night before the test to memorize (and understand) them.

#### What Geometry topics are on the SAT?

The SAT Math Test has 2 sections: a no-calculator section (20 questions) and a calculator section (38 questions). Test-takers are likely to encounter geometry questions on both sections. There are no proofs on the SAT, but the test does include questions that assess your understanding of the key concepts in the geometry of lines, angles, triangles, circles, and other geometric objects. Other questions may also ask you to find the area, surface area, or volume of an abstract figure or a real-life object.

#### Are there any apps that will help me solve Geometry problems?

Yes! Here is a list of the best apps as well as graphing calculators to help you in your Geometry (and other math) courses!

All are available on iPhone, iPad, and Android:

**Photomath**
**Mathway**
**Geometry Solver**
**WolframAlpha**

#### What are jobs that involve Geometry?

If you find yourself excelling in and enjoying geometry, there are several career paths available to you. In order to be qualified for jobs in this field, you will need a Bachelor’s (and in most cases, a Master’s) degree in fields such as Applied Mathematics, Data Science, Mathematics, Data Analytics, and Information Systems.

**Architects** utilize geometric principles while designing layouts for their ongoing projects, which can include buildings, electrical systems, and plumbing architecture.

**Cartographers** utilize geographic data to create or update maps for use in education, as well as environmental presentations.

**Photogrammetrists** use the same information to draw base maps, allowing the layering of data. Both cartographers and photogrammetrists help those who work in urban and regional planning and use geometry to create documents.

**Drafters** use the same geometric knowledge and applications as architects and engineers, but create design plans with the use of computer-aided design software.

**Mechanical** engineers, some of the most diversified engineers, use a multitude of geometric concepts to design mechanical devices, or update existing structures. They can create anything from elevators and escalators to transfer systems or air conditioners.

**Surveyors** use geometry to take exact measurements of boundaries for different types of property. Comparing their measurements to previously existing records is a vital part of their job.

**Urban and regional planners** rely on the same geometry practices used by surveyors when examining the positives and negatives of introducing new and updated plans for a community.