Some auxiliary elements unite previously unrelated components of the original diagram others divide a given complex entity into manageable ones.

We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Implications for further educational research and mathematics instruction are proposed.ĪB - 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. the two sides forming the right angle of a right triangle. the process of developing a general principle from accepted, particular facts. but if clause of a theorem that is assumed to be true. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. the side opposite the right angle the longest side of a right triangle, hypothesis. N2 - 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. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. T1 - Focusing attention on auxiliary lines when introduced into geometric problems

Auxiliary line geometry definition