Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Aliza Malek, Moshe Stupel and Avi Sigler
Pages: [67] - [87]
Received Date: November 24, 2016; Revised January 5, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121744
Theorems and claims in Mathematics in general, and in geometry in particular, are an inseparable part of the material and of the mathematical education imparted to high school students. Proving claims is a central component in geometry classes. Students acquire knowledge on the properties of shapes and bodies and make use of these properties in proving different claims. For each claim, one can formulate the converse claim, which in some cases may be right and in others not. Teachers do not always make use of the opportunity to formulate with the students the converse claim and to examine its truth by achieving a proof or finding an example to the contrary if it is not true. The present paper presents eight interesting mathematical claims in geometry, were for each claim and converse claim complete proofs are given using different mathematical tools, including indirect proofs. Teachers can make use of such and other examples to expose the students to the claim and the converse claim and to the methods for dealing with various methods of proof and of preventing mistakes.
a theorem and a converse theorem, different methods in proof.
