Important Lines in Triangles A Computer-Assisted Lesson Walther Unterleitner, Manfred Piok, Maximilian Gartner Intention The pupils construct the most important features of triangles with the help of GeoGebra and study their characteristics by changing the shape of the triangles. Four to six lessons are recommended for this tasks depending on the pupils‘ knowledge of GeoGebra. Background of Subject Matter The most important points in triangles (Point of intersection of perpendicular bisectors as circumcentre, point of intersection of angle bisectors as incentre, centroid (centre of mass), and point of intersection of altitudes as orthocentre) are being constructed. The location of these points varies depending on the shape of the triangle; three out of the four are located on the Euler line. GeoGebra enables the pupils to test various cases and through this draw conclusions. Additionally, faster pupils can try to find the Fermat point. Methodical Advice In order to work with this learning environment, pupils require knowledge of the following terms: Perpendicular bisector Angle bisector Median Altitude Distance The first task can be used for demonstration purposes in order to explain GeoGebra’s tools. Pupils ought to work alone or together with a partner. Performance Rating The pupils solve the tasks and write down their thoughts and results on the computer. The produced graphs from GeoGebra will be added to the document. This document will then be graded according to content, clarity, and the proficiency in construction and argumentation.
Important Lines in Triangles A Computer-Assisted Lesson Walther Unterleitner, Manfred Piok, Maximilian Gartner Intention The pupils construct the most important features of triangles with the help of GeoGebra and study their characteristics by changing the shape of the triangles. Four to six lessons are recommended for this tasks depending on the pupils‘ knowledge of GeoGebra. Background of Subject Matter The most important points in triangles (Point of intersection of perpendicular bisectors as circumcentre, point of intersection of angle bisectors as incentre, centroid (centre of mass), and point of intersection of altitudes as orthocentre) are being constructed. The location of these points varies depending on the shape of the triangle; three out of the four are located on the Euler line. GeoGebra enables the pupils to test various cases and through this draw conclusions. Additionally, faster pupils can try to find the Fermat point. Methodical Advice In order to work with this learning environment, pupils require knowledge of the following terms: Perpendicular bisector Angle bisector Median Altitude Distance The first task can be used for demonstration purposes in order to explain GeoGebra’s tools. Pupils ought to work alone or together with a partner. Performance Rating The pupils solve the tasks and write down their thoughts and results on the computer. The produced graphs from GeoGebra will be added to the document. This document will then be graded according to content, clarity, and the proficiency in construction and argumentation.
Important_Lines_in_Triangles.docx