Elementary College Geometry - 2021 ed.

Reviewed by Larissa Shatalova, Instructor, PhD, Math department, Lane Community College on 9/14/25

Comprehensiveness rating: 5 see less

The textbook Elementary College Geometry (2021 ed.) offers a comprehensive and well-balanced selection of topics, suitable both for a full introductory geometry course and as a modular supplement to other mathematical disciplines.
Key thematic areas include:
Basic geometric definitions (points, lines, planes, angles),
Congruence and similarity,
Triangles and quadrilaterals,
Circles and polygons,
Area and perimeter of plane figures,
Surface area and volume of solids,
Coordinate geometry, and
Logical reasoning and proofs.
Each topic is introduced with clear explanations, step-by-step examples, and practice problems that reinforce conceptual understanding. The structure allows instructors to select individual chapters to reinforce specific topics in other courses, such as:
Using triangle congruence in algebra or trigonometry,
Exploring coordinate geometry in pre-calculus or data visualization,
Introducing deductive logic in liberal arts math.
The inclusion of review sections and solution checking strategies further enhances the book’s comprehensiveness, making it not only a source of information but also a tool for developing mathematical confidence and independence.

Content Accuracy rating: 5

The textbook demonstrates a high level of mathematical accuracy and precision throughout. Definitions are stated clearly, theorems are properly formulated and attributed, and logical reasoning is consistent with standard mathematical practices.
Diagrams are carefully constructed and correctly labeled, supporting the explanations without oversimplifying key ideas.
Terminology is used consistently and appropriately, making the book suitable both for beginners and as a reference for more advanced learners.
Worked examples follow logically sound steps and include no computational or conceptual errors.
Exercises are well-aligned with the chapter goals, and answer keys (when provided) reinforce correct reasoning without encouraging rote memorization.
Importantly, the book manages to balance accessibility with rigor, which is often difficult to achieve in introductory geometry texts. It avoids common pitfalls such as vague visual arguments or over-reliance on intuition, instead guiding students toward formal mathematical thinking in a friendly, structured way.

Relevance/Longevity rating: 5

The content of Elementary College Geometry (2021 ed.) is highly relevant to the needs of today’s mathematics curriculum, despite the unfortunate trend of removing stand-alone geometry courses in many colleges.
Geometry remains a foundational component of mathematical reasoning, spatial understanding, and problem-solving — skills that are essential across numerous disciplines including:
Algebra and trigonometry (e.g., triangle properties, coordinate systems),
Pre-calculus and calculus (e.g., limits involving area and volume),
Liberal arts math (e.g., logic, reasoning, visual proof structures),
Technical programs (e.g., drafting, architecture, computer science),
And even standardized testing and teacher preparation programs.
This textbook fills a growing gap by offering a flexible, modular resource that instructors can integrate into various courses without requiring a full-term geometry offering.
Furthermore, its OER format ensures broad accessibility and affordability, aligning with current equity-focused educational initiatives.
In an era where geometric intuition is often assumed but rarely taught, this textbook provides relevant, structured, and accessible support for both students and instructors seeking to strengthen geometric thinking in a wide variety of learning contexts.

Clarity rating: 5

One of the standout features of Elementary College Geometry (2021 ed.) is its remarkable clarity in both exposition and structure. The author uses simple, direct language without sacrificing mathematical precision, making the content highly accessible to a wide range of learners — including those who may not have strong algebraic or spatial backgrounds.
Each concept is introduced gradually, with clear motivation, followed by intuitive diagrams and step-by-step examples.
Definitions and theorems are presented in a visually distinct format, which supports scanning and retention.
The logical flow from explanation → example → practice → review helps reduce cognitive overload and encourages deep comprehension rather than surface memorization.
Particularly commendable is the author’s ability to balance formal mathematical rigor with an informal, welcoming tone. The text does not assume prior mastery — instead, it guides the learner gently toward geometric understanding.
This clarity makes the book not only suitable for traditional classroom use, but also ideal for:
Self-study,
Tutoring sessions,
Supplemental reading for non-STEM students in general math courses.

Consistency rating: 5

Elementary College Geometry (2021 ed.) maintains a high degree of consistency across chapters (Chapter 3 uses the same triangle notation introduced in Chapter 1) , examples, terminology, and visual design.
Mathematical notation is applied uniformly throughout the text, reducing confusion and supporting transfer of learning from one topic to the next.
The structure of each chapter follows a predictable and pedagogically sound pattern:
Clear introduction of concepts,
Followed by illustrative examples,
Then exercises and review sections.
Terminology is introduced once, then used consistently without unnecessary variation, which is particularly helpful for non-native English speakers or students with learning differences.
The visual formatting (such as how definitions, theorems, and key steps are boxed or highlighted) remains consistent from beginning to end, providing cognitive scaffolding and reinforcing the structure of mathematical arguments.
Furthermore, the instructional tone is steady — approachable but precise — giving the textbook a cohesive voice that supports student trust and engagement.

Modularity rating: 5

One of the most valuable features of Elementary College Geometry (2021 ed.) is its strong modular design. Each chapter is self-contained and thematically focused, allowing instructors to easily extract and integrate individual sections into other math courses without requiring prior knowledge of the entire text.
Instructors can assign a single chapter — such as triangle congruence, area and perimeter, or logical proofs — to support specific units in algebra, trigonometry, or liberal arts math.
Chapters begin with a clear introduction and end with practice and review, making them ideal for stand-alone use in tutoring centers, workshops, or supplemental learning modules.
There are no excessive cross-references that depend on material from earlier chapters, which allows for flexibility in sequence.
This modularity also makes the book highly suitable for custom course shells in LMS platforms (e.g., Canvas, Moodle), where chapters can be uploaded and reorganized as needed.

Because of its modular structure, the book aligns well with current trends in competency-based education and flipped classroom models, where instructors may choose to focus on specific skills or concepts rather than progressing linearly through a textbook.

Organization/Structure/Flow rating: 5

Elementary College Geometry (2021 ed.) is organized in a clear, logical, and pedagogically sound manner. The progression of topics reflects a natural development of geometric reasoning, starting from foundational definitions and building gradually toward more complex ideas.
The book begins with basic elements of geometry — points, lines, angles — and moves steadily through triangles, quadrilaterals, circles, solids, coordinate geometry, and proofs.
Each chapter follows a consistent internal structure:
Introductory explanations to set the stage,
Worked examples to illustrate new concepts,
Practice exercises to reinforce learning,
And often a review or summary to consolidate understanding.
The chapter sequencing supports cumulative learning, where each new topic builds on the previous without abrupt transitions or unnecessary repetition. Even when chapters are used out of order (thanks to its modularity), the internal organization remains coherent and learner-friendly.
Headers, typography, and visual cues (such as boxed theorems and step-by-step diagrams) are well-designed to guide students through the content with minimal friction.
This thoughtful organization makes the textbook suitable not only for semester-long courses, but also for compressed, modular, or self-paced formats, where clarity and navigability are essential.

Interface rating: 5

The interface and formatting of Elementary College Geometry (2021 ed.) are clear, functional, and highly readable in both digital and printed formats.
The PDF layout is clean, with generous spacing, consistent fonts, and logical use of headings and subheadings. This supports ease of navigation and reduces visual fatigue, especially for students reading on screens.
Mathematical expressions are typeset clearly, with no rendering errors or awkward line breaks, making the material easy to follow even in complex proofs.
Diagrams are well-integrated with the text — not just decorative, but truly supportive of the explanations. Labels are legible, and figures are placed close to the relevant discussion.
Internal page navigation is intuitive, with numbered sections and a hyperlinked table of contents that works reliably in digital view.
The file opens smoothly on most devices (laptops, tablets, even smartphones), and prints well for those who prefer physical copies.
Although the book is not interactive (as some HTML-based OERs may be), its static interface is stable and distraction-free, which can be a benefit in focused study environments.

Grammatical Errors rating: 5

The textbook Elementary College Geometry (2021 ed.) exhibits a high level of grammatical correctness and editorial polish.
Sentences are well-structured and free of distracting grammatical errors, allowing students to focus on the mathematical content rather than deciphering unclear phrasing.
The writing maintains a consistent academic tone, while remaining accessible and conversational enough for introductory learners.
Mathematical terminology is used appropriately and integrated seamlessly into explanations, without awkward transitions or misuse.
There are no noticeable typos, spelling mistakes, or punctuation issues across chapters reviewed — a rare and commendable trait in OER materials.
This grammatical clarity enhances the overall credibility and professionalism of the textbook and supports its use in both formal instruction and independent learning.

Cultural Relevance rating: 5

While Elementary College Geometry (2021 ed.) is a traditional mathematics text focused on abstract geometric concepts, it maintains a culturally neutral tone and avoids biased or exclusionary language. The problems and examples are mathematically universal, without reliance on culturally specific contexts, which ensures broad accessibility for students from diverse backgrounds. There are no instances of gendered, stereotypical, or culturally insensitive language, and the visuals are purely mathematical, minimizing potential distractions or biases. Although the book does not actively incorporate culturally responsive pedagogy (e.g., real-world examples tied to diverse cultures or student experiences), its clarity and neutrality make it adaptable for inclusive instruction. Instructors who wish to bring in cultural context can easily supplement the textbook with their own examples or applications, without needing to "work around" any problematic content.

Final Recommendation
Based on a detailed review of Elementary College Geometry (2021 ed.) by Henry Africk, I will be recommending this textbook to our department as a supplementary resource across multiple mathematics courses.
While our current curriculum does not include a dedicated geometry course, the absence of formal geometric instruction creates noticeable gaps in student understanding — particularly in areas requiring spatial reasoning, deductive logic, or visual proof structures.
This textbook:
provides clear and accurate explanations,
offers flexible modular use,
maintains high editorial quality and pedagogical clarity,
and remains culturally neutral and accessible.
Whether integrated as individual chapters in courses like Math 98, Math 105Z, or Math 111, or used for tutoring and self-study, Elementary College Geometry serves as a strong foundation for reintroducing essential geometric thinking into our program — without needing to create a new course from scratch.
Instructors across the department can benefit from its clarity, structure, and adaptability. I strongly recommend that it be included in our list of officially supported OER materials and made available to students as an optional enrichment resource.