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Special Properties of a Triangle with an Angle of 60°

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Abstract

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.

In this article, we consider 35 special properties of a triangle with an angle of 60°. These properties relate to the most different elements of the triangle: sides, angles, area, circumradius and inradius, various singular points of the triangle, and their mutual location. Some of them are quite elementary and can be used in the study of geometry by high school students. Others are more complex and involve concepts outside of the school geometry course (Fermat point, isodynamic point, symmedian, and others). They can be helpful in teaching mathematics teachers at teacher training colleges and universities and can be used for mathematical enrichment and the expansion of the ‘toolbox’ available to them.

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Author information

Authors and Affiliations

  1. Gordon College and Shaanan College, Haifa, Israel

    Moshe Stupel

  2. Western Galilee College, Acre, Israel

    Victor Oxman

  3. Shaanan College, Haifa, Israel

    Avi Sigler

Authors
  1. Moshe Stupel
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  2. Victor Oxman
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  3. Avi Sigler
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Corresponding authors

Correspondence to Moshe Stupel, Victor Oxman or Avi Sigler.

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No potential conflict of interest was reported by the authors.

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Stupel, M., Oxman, V. & Sigler, A. Special Properties of a Triangle with an Angle of 60°. Reson 26, 1141–1152 (2021). https://doi.org/10.1007/s12045-021-1213-1

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  • DOI: https://doi.org/10.1007/s12045-021-1213-1

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