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ERIC Number: EJ1035567
Record Type: Journal
Publication Date: 2014-Aug
Pages: 7
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0025-5769
EISSN: N/A
Available Date: N/A
Triangles from Three Points
Nirode, Wayne
Mathematics Teacher, v108 n1 p32-38 Aug 2014
Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th International Congress on Mathematics Education. Jun referenced Wernick's (1982) original work in which he posed 139 unique problems. In each problem, three points are chosen from the following set of sixteen points--the three vertices of a triangle, the four classic points of concurrency (i.e., centroid, circumcenter, incenter, and orthocenter), the three midpoints, the three perpendicular feet, and the three feet of the angle bisectors The task is to locate, if possible, the three vertices of the triangle. For example, one possible version of the problem is to locate the other two vertices of a triangle given a vertex, the orthocenter, and the centroid. In this article Nirode describes how he implemented Wernick's problems in his instruction with his freshman honors geometry students in two distinct ways. First, he gave students numeric coordinates for three points and asked them to find the coordinates of the vertices of the triangle. Second, he followed Jun's suggestion to use dynamic geometry software (DGS) and gave students problems to complete as a project using The Geometer's Sketchpad® (GSP). (Other versions of DGS also could be used, such as GeoGebra, which is free.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Ohio
Grant or Contract Numbers: N/A
Author Affiliations: N/A