Publication Date


Document Type


First Advisor

Hellmich, Eugene W. (Eugene William), 1902-

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Education


Hart; Walter W. (Walter Wilson); 1879-; Geometry; Plane


The purpose of this study is to determine which theorems and assumptions are useful in proving other theorems and original exercises in Walter W. Hart's Plane Geometry. Every year high school students sign up for plane geometry with great enthusiasm, expecting to learn better the art of reasoning and to improve themselves as students and citizens. Then, after six or eight weeks, the slow-learning students run into difficulty because they are required to remember many more than they are capable of remembering. This, or course, takes much enjoyment out of the course for them, and many become frustrated and lose their enthusiasm and interest. To help the slow learners avoid experiencing this difficulty in years to come, the author of this paper has determined, to the best of his ability, those theorems which are frequently needed, therefore defined as "very useful”; those less frequently needed, classified as ”useful", and those that are very seldom or never needed, and termed "less useful". The words frequently, less frequently, and very seldom, will be defined later. In determining the use of theorems and assumptions, the author has roved all the theorems and original exercises in the book and has carefully recorded the reasons needed in the proofs. Many exercises and theorems can be proved several ways. In this study, only the way in which it was thought that the student would most likely do the problem was considered. If the same reason was used more than once in any proof, it was recorded only once. In doing constructions, careful record was made of the theorems and assumptions necessary in the construction, as well as those needed in the proof of the construction. In working out numerical exercises, careful record was made of the theorems and assumptions that the student would have to know if he were required to prove the numerical exercise.


34 pages




Northern Illinois University

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