Harold Jacobs has managed to write a user-friendly geometry text that is heavy on logic and proofs. This is one book where you don’t want to skip the introduction that fills students in on the influence of Euclid and teaches them the basics of construction with a straight edge and compass.
In the third edition, the first chapter is an introduction to vocabulary, tools, and basic ideas of geometry. However, it ends with a lesson titled, “We Can’t Go On Like This,” a lesson that takes students through some intriguing problems to demonstrate the necessity for a logical approach to geometry.
Then, in the second chapter, Jacob begins to teach logic. Many people cite the value of geometry as being the development of logical thinking skills. Jacobs takes this idea seriously, ensuring that students are truly tuned in to logical thinking before tackling other geometry topics. Given the foundation in logic, students then immediately begin work with proofs, which continues throughout the text.
Jacobs uses entertaining illustrations (including cartoons), as well as practical applications and engaging word problems. For example, the lesson on similar figures and ratio begins with a comparison of movie and television screens, including the letter-box option that changes the ratio.
Topic arrangement is different than I have seen in most texts. For instance, work with circles follows introductory lessons on trigonometry. The trigonometry is introduced as a natural progression in the study of triangles, so this is not really an outlandish arrangement. Even if the arrangement is unusual, there is a clear continuity to topics, building one upon another.
There are sixteen chapters in the book, with each chapter divided into a number of lessons. Each lesson has three problem sets. All students should try to complete the first two sets, but skip the second set for struggling students. The third set frequently features intriguing investigations, but these should be used as a challenge for better students who have the time. A summary and review at the end of each chapter includes specific algebra review.
Construction activities (using straight edge and compass) are minimal. Because of this and the emphasis on logic, I recommend this text for abstract thinkers rather than hands-on learners. But I suspect that even some students who struggle with the logic will like this text because the presentation is so appealing.
Problems from SAT tests are interspersed throughout the exercises. They are labeled as such so students preparing for the test can be sure to master these.
Selected answers for about one fourth to one third of the problems from each lesson (selected in no numerical sequence) are at the back of the student text. All answers are in the instructor’s guide. A separate test bank is available in either book or CD-ROM format (both Windows and Mac versions on one disk).
You might be interested in using Ask Dr. Callahan Geometry DVD set that teaches Jacob's geometry course.