08-30-2026, 01:48 PM
Elementary College Geometry
Author: Henry Africk
Publication date: 2021
Publisher: CUNY Academic Works, New York City College of Technology
Subject: Euclidean / Plane Geometry and Trigonometry
License: CC BY-NC-SA
Level: Introductory college mathematics; prerequisite is roughly one semester of algebra.
Summary
Elementary College Geometry is an accessible introduction to classical Euclidean plane geometry, designed primarily for students who need geometric foundations for later work in algebra, trigonometry, precalculus, calculus, or technical subjects. Africk deliberately keeps the number of definitions and theorems relatively small and emphasizes using geometric principles to solve numerical problems rather than developing a highly formal axiomatic treatment. Proofs are generally short and intuitive, closer to the style of a precalculus textbook than to a proof-oriented university geometry course.
The book progresses through seven principal areas: lines, angles and triangles; congruent triangles; quadrilaterals; similar triangles; trigonometry and right triangles; area and perimeter; and regular polygons and circles. Important ideas include triangle congruence and similarity, angle relationships, properties of parallelograms and other quadrilaterals, the Pythagorean theorem, ratios in similar figures, and elementary trigonometric functions such as $\sin\theta$, $\cos\theta$, and $\tan\theta$. Geometry is therefore treated not merely as a collection of facts, but as a practical system for calculating unknown lengths, angles, areas, and other quantities.
Pedagogically, the text is strongly oriented toward worked examples and exercises. Problems are arranged in pairs so instructors can assign either odd- or even-numbered exercises, and the material can be taught deductively even though formal theorem proving is not the main objective. A 2025 review in the Open Textbook Library rated the book highly for comprehensiveness, accuracy, clarity, consistency, modularity, and organization, noting that chapters can also be used independently as supplementary material in other mathematics courses.
Key takeaways
Open Textbook Library – Elementary College Geometry
Author: Henry Africk
Publication date: 2021
Publisher: CUNY Academic Works, New York City College of Technology
Subject: Euclidean / Plane Geometry and Trigonometry
License: CC BY-NC-SA
Level: Introductory college mathematics; prerequisite is roughly one semester of algebra.
Summary
Elementary College Geometry is an accessible introduction to classical Euclidean plane geometry, designed primarily for students who need geometric foundations for later work in algebra, trigonometry, precalculus, calculus, or technical subjects. Africk deliberately keeps the number of definitions and theorems relatively small and emphasizes using geometric principles to solve numerical problems rather than developing a highly formal axiomatic treatment. Proofs are generally short and intuitive, closer to the style of a precalculus textbook than to a proof-oriented university geometry course.
The book progresses through seven principal areas: lines, angles and triangles; congruent triangles; quadrilaterals; similar triangles; trigonometry and right triangles; area and perimeter; and regular polygons and circles. Important ideas include triangle congruence and similarity, angle relationships, properties of parallelograms and other quadrilaterals, the Pythagorean theorem, ratios in similar figures, and elementary trigonometric functions such as $\sin\theta$, $\cos\theta$, and $\tan\theta$. Geometry is therefore treated not merely as a collection of facts, but as a practical system for calculating unknown lengths, angles, areas, and other quantities.
Pedagogically, the text is strongly oriented toward worked examples and exercises. Problems are arranged in pairs so instructors can assign either odd- or even-numbered exercises, and the material can be taught deductively even though formal theorem proving is not the main objective. A 2025 review in the Open Textbook Library rated the book highly for comprehensiveness, accuracy, clarity, consistency, modularity, and organization, noting that chapters can also be used independently as supplementary material in other mathematics courses.
Key takeaways
- Practical rather than highly axiomatic: the emphasis is on solving geometry problems rather than mastering formal proof techniques.
- Strong preparation for trigonometry: similarity, right triangles, the Pythagorean theorem, and trigonometric ratios provide a natural bridge into precalculus.
- Suitable for self-study: explanations, diagrams, worked examples, and exercises make it approachable for students refreshing their geometry.
- Best suited to introductory study: students seeking advanced Euclidean geometry, transformations, projective geometry, or rigorous axiomatic treatments will need a more advanced text afterward.
Open Textbook Library – Elementary College Geometry
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘