Priečky lichobežníka v prostredí programu GeoGebra
Trapezoid’s Transversals in GeoGebra Environment
Abstract
In this article we present a few possibilities how to use special GeoGebra commands and tools. We focus on certain relations among geometric objects in a planar construction, especially for the trapezoid and its transversals. Dynamic geometry environment of GeoGebra software for symbolic checks of any relations allowing derivation, proving and discovering of theorems related to constructed geometric figures. Approach of using a low-level GeoGebra automated reasoning tools (LocusEquation, Relation, Prove, ProveDetails) is presented on some geometric situations for trapezoid transversals. Moreover, in all cases verifications and proving of the constructive geometric facts based on the method of calculation of area are included, too.
- Keywords
- GeoGebra, trapezoid, transversals, area method
- Classification
- H30, R20
References
Kovács, Z. (2018). Automated reasoning tools in GeoGebra: A new approach for experiments in planar geometry. South Bohemia Mathematical Letters 25, 48-65
Kovács, Z. (2015). Computer Based Conjectures and Proofs in Teaching Euclidean Geometry. PhD thesis, Johannes Kepler University, Linz, Austria
Kovács, Z. (2015). The Relation Tool in GeoGebra 5. In: Botana F., Quaresma P. (eds) Automated Deduction in Geometry. ADG 2014. Lecture Notes in Computer Science, Vol. 9201. Springer
Billich, M. (2015). The Area Method and Proving Plane Geometry Theorems. In: Mityushev V., Ruzhansky M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics. Birkhäuser
Janičić, P., Narboux, J., Quaresma, P. (2012). The Area Method. Journal of Automated Reasoning 48, 489–532
Quaresma, P., Janičić, P. (2009).The Area Method. Rigorous Proofs of Lemmas in Hilbert’s Style Axioms Systems. Technical Report TR2006/001, Center for Informatics and Systems of the University of Coimbra
Kovács, Z. (2020). GeoGebra Discovery. A GitHub project Dostupné na internete: https://github.com/kovzol/geogebra-discovery. Citované online: 26.3.2021.
Kovács, Z. (2015). Computer Based Conjectures and Proofs in Teaching Euclidean Geometry. PhD thesis, Johannes Kepler University, Linz, Austria
Kovács, Z. (2015). The Relation Tool in GeoGebra 5. In: Botana F., Quaresma P. (eds) Automated Deduction in Geometry. ADG 2014. Lecture Notes in Computer Science, Vol. 9201. Springer
Billich, M. (2015). The Area Method and Proving Plane Geometry Theorems. In: Mityushev V., Ruzhansky M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics. Birkhäuser
Janičić, P., Narboux, J., Quaresma, P. (2012). The Area Method. Journal of Automated Reasoning 48, 489–532
Quaresma, P., Janičić, P. (2009).The Area Method. Rigorous Proofs of Lemmas in Hilbert’s Style Axioms Systems. Technical Report TR2006/001, Center for Informatics and Systems of the University of Coimbra
Kovács, Z. (2020). GeoGebra Discovery. A GitHub project Dostupné na internete: https://github.com/kovzol/geogebra-discovery. Citované online: 26.3.2021.