Proving the Equkaity of the Base Angles of an Isosceles Triangle

1929 ◽  
Vol 22 (6) ◽  
pp. 318-319
Author(s):  
Joseph A. Nyberg
Keyword(s):  
Mathematics Teacher ◽  
Isosceles Triangle ◽  
Plane Geometry ◽  
Angle Bisector ◽  
Significant Step

In a recent paper (A Different Beginning for Plane Geometry, by H. C. Christofferson, MATHEMATICS TEACHER, Dec., 1928) much emphasis is placed on the fact that the existence of an angle bisector must be assumed in proving that tho base angles of an isosceles triangle are equal. Because of this assumption it is argued that, we could better begin by assuming triangles congruent if the corresponding sides are equal. The following is a proof of the equality of the base angles of an isosceles triangle without the use of tho angle bisector. Since the quqestion seems important I present the proof with some detail. Step 4 is the significant step.

A Fallacy in Geometry Reasoning

1930 ◽  
Vol 23 (1) ◽  
pp. 19-22
Author(s):  
H. C. Christofferson
Keyword(s):  
Mathematics Teacher ◽  
Isosceles Triangle ◽  
Angle Bisector ◽  
Usual Order

In the mathematics teacher for December, 1928, I attempted to expose a weakness in the usual proofs of beginning geometry and advocated a new and slightly different beginning which at the same time bas the virtue of being more simple. The usual order of proofs is (1) congruence by side-angle-side; (2) congruence by angle-sideangle; (3) the theorem that the angles opposite the equal sides of an isosceles triangle are equal; (4) congruence by three sides; and (5) sometime later, the construction of an angle bisector and of an angle equal to a given angle. We are concerned here with only (3), (4), and (5).

Tips for Beginners: Optional proofs of theorems in plane geometry

1955 ◽  
Vol 48 (8) ◽  
pp. 578-580
Author(s):  
Francis G. Lankford
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Deductive Proof

This department of The Mathematics Teacher for October contained an article on “Helping Pupils Use Proofs of Theorems in Geometry.” There, some suggestions were given for helping pupils to understand the nature of a deductive proof and to develop the ability to prove theorems independently.

The War on Euclid

1942 ◽  
Vol 35 (5) ◽  
pp. 205-207
Author(s):  
Charles Salkind
Keyword(s):  
Mathematics Teacher ◽  
Progressive Education ◽  
Turn Of The Century ◽  
Joint Commission ◽  
Plane Geometry ◽  
Education Association ◽  
History Of ◽  
The Joint Commission

To recite the history of the attempts, since even before the turn of the century, to modify the method and content of the Plane Geometry Course or “Euclid,” is to invite upon oneself the charge of banality. From the early efforts of Perry and Russell in England, of Laisant in France, of Klein in Germany, of Moore and Hedrick in our own country, to the two most recent reports by the Progressive Education Association and the Joint Commission, through article after article in The Mathematics Teacher and other professional magazines, the battle for reform has been and still is raging.

The Art of Teaching: A New Technique in Handling the Congruence Theorems in Plane Geometry

1943 ◽  
Vol 36 (5) ◽  
pp. 237-239
Author(s):  
Ralph C. Miller
Keyword(s):  
Isosceles Triangle ◽  
Usual Method ◽  
Plane Geometry ◽  
New Technique ◽  
The Third ◽  
Art Of Teaching ◽  
A New Technique ◽  
Congruence Theorem

The Usual method of proof employed in the congruence theorems kills, rather than stimulates, the interest of many students being introduced to geometry. The customary method of superposition applies some very nice axioms and postulates, but leaves the student mystified as to what it is all about. The fact the assumption, that an angle can be bisected, is used to prove the isosceles triangle theorem, which is used to prove the third congruence theorem (s.s.s. equals s.s.s.), which in turn is used to prove the original assumption (that an angle can be bisected) should contribute much to the added confusion of an alert student.

A Reply to Mr. Nygaard

1942 ◽  
Vol 35 (4) ◽  
pp. 179-181
Author(s):  
Norman N. Royall
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
National Council ◽  
School Year ◽  
Student Chapter ◽  
Group I

I have read, with ever increasing incredulity, an article in the October (1941) issue of The Mathematics Teacher entitled “A Functional Revision of Plane Geometry” by P. H. Nygaard. Mr. Nygaard's article is such a glaring example of the type of discussion which finds its way into print today to the mortal harm of sound instruction in mathematics that I can not let it pass unchallenged. We have here at Winthrop a student chapter of the National Council of Teachers of Mathematics into the hands of whose members there comes each month during the school year a copy of The Mathematics Teacher. Since I am the faculty sponsor of this group I can for them correct the enors in Mr. Nygaard's essay. The effect of this correction is, however, limited by the range of my voice; therefore, I hope that my reply may have full publicity in The Mathematics Teacher to the end that I may reach the audience afforded to Mr. Nygaard.

More new exercises in plane geometry

1957 ◽  
Vol 50 (5) ◽  
pp. 330-339
Author(s):  
_ _
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Similar Material ◽  
Wide Range ◽  
Mathematics Student ◽  
New Type

The stock of geometrical exercises of the new type introduced in the February 1957 issue of The Mathematics Teacher is here increased so that a wide range of suggested problems is opened to the teacher of geometry.This paper, the last in a series of five devoted to the cutting of squares, also supplements similar material inThe Mathematics Student Journal for April1957.

Tessellations and the Art of M. C. Escher

1984 ◽  
Vol 31 (5) ◽  
pp. 54-55
Author(s):  
Betty K. Zurstadt
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Upper Elementary ◽  
Elementary Years ◽  
The World

Relating mathematics to the world around us is one of the goals of the mathematics teacher. Plane geometry can be made relevant in the upper elementary years with a study of Escher's tessellations and how he created them.

Individual Work in Plane Geometry

1930 ◽  
Vol 23 (3) ◽  
pp. 155-160
Author(s):  
Jas. H Zant
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Ninth Grade ◽  
The State ◽  
Plane Geometry ◽  
Text Book ◽  
Teachers College ◽  
Individual Work ◽  
Individual Instruction ◽  
Work Done

In the October 1929 number of the Mathematics Teacher there appeared a report of individual work done in ninth grade algebra1. The following report may be of interest as a description of an attempt to teach plane geometry by an individual instruction method. It was used in the Russell High School of the Southeastern State Teachers College, Durant, Oklahoma during the winter and spring of 1927-28. The class used was composed of about twentyfive members which were all the pupils taking geometry in this particular school. The text book in use was the state adopted text of Oklahoma, Newell and Harper's Plane Geometry, published by RowPeterson and Company.

The Art of Teaching A New Department

1936 ◽  
Vol 29 (7) ◽  
pp. 346
Author(s):  
Margaret Amig
Keyword(s):  
Isosceles Triangle ◽  
Plane Geometry ◽  
Formal Proofs ◽  
Common Error ◽  
Formal Geometry ◽  
Art Of Teaching

I have found a very slight departure from the usual arrangement of a proposition in plane geometry, very effective in helping pupils to surmount a common difficulty and to avoid a common error. Most beginners find it hard to see why formal proofs of geometric facts are necessary and some are openly rebellious at the idea of giving tedious demonstrations of the truth of very obvious conclusions. Furthermore many pupils approach formal geometry with a background of intuitive geometry and facts retained from that study are likely to increase the pupil's reluctance to substitute reasoning for inspection. The accepted a rrangement of a proposition—first theorem, then figure, then proof—adds, it seems to me, to his confusion. Why, he asks, should one write at the top of the page or recite that the base angles of an isosceles triangle are equal and then proceed to prove that it is true?

Tips for Beginners: An aid to writing deductive proofs in plane geometry

1958 ◽  
Vol 51 (4) ◽  
pp. 303-305
Author(s):  
John F. Schacht
Keyword(s):  
High School ◽  
High School Students ◽  
Mathematics Teacher ◽  
Recent Article ◽  
Plane Geometry ◽  
School Students

In a recent article in The Mathematics Teacher, Rosskopf and Exner suggest that “… teachers and textbooks should do a better job of introducing high school students to the concepts of logic.”1

Sign in / Sign up

Export Citation Format

Share Document