Focusing attention on auxiliary lines when introduced into geometric problems

Alik Palatnik*, Avi Sigler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students’ attention. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Some auxiliary elements unite previously unrelated components of the original diagram; others divide a given complex entity into manageable ones. Implications for further educational research and mathematics instruction are proposed.

Original languageAmerican English
Pages (from-to)202-215
Number of pages14
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number2
StatePublished - 17 Feb 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.


  • Auxiliary lines
  • high-school geometry
  • problem-solving
  • shifts of attention


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