Presentació

[br][justify]El programari lliure GeoGebra és una eina molt potent per treballar diferents parts de les matemàtiques.[br][br]El seu dinamisme permet que sigui un recurs molt útil per a la comprovació de propietats i conjectures, com també per a la resolució de problemes de tot tipus.[br][br]En aquest taller ens centrarem en la construcció de figures geomètriques dinàmiques que permetin conjecturar i comprovar propietats de caràcter geomètric.[br][br]Per començar, farem una introducció al programa; d'aquesta manera, qui no el conegui, també podrà arribar a les construccions proposades. La facilitat del seu ús ho permetrà.[br][br]Enllaç a la pàgina oficial de GeoGebra: [url=https://www.geogebra.org/]https://www.geogebra.org/[/url][/justify]

Els quatre centres del triangle i la recta d'Euler

En qualsevol triangle:
[b][br][br]Baricentre:[/b] Punt de tall de les [i]mitjanes.[sup]1[/sup][/i][br][br][b]Ortocentre:[/b] Punt de tall de les [i]altures.[sup]2[/sup][/i][br][br][b]Circumcentre:[/b] Punt de tall de les [i]mediatrius.[sup]3[/sup][/i][br][br][b]Incentre:[/b] Punt de tall de les [i]bisectrius.[sup]4[br][br][/sup][/i]___________________________________[br][br][sup]1[/sup][b]mitjana:[/b] segment que uneix un vèrtex i el punt mitjà del costat oposat a aquest vèrtex.[br][br][sup]2[/sup][b]altura:[/b] segment perpendicular a un cotat fins el vèrtex oposat a aquest costat.[br][br][sup]3[/sup][b]mediatriu:[/b] recta perpendicular a un costat que passa pel seu punt mitjà.[br][br][sup]4[/sup][b]bisectriu:[/b] recta que passa per un vèrtex i divideix en dos parts iguals l'angle que determina aquest vèrtex.[br][br]___________________________________[br][br][b]Baricentre, Ortocentre i Circumcentre[/b] estan aliniats, i la recta que els conté s'anomena [b]recta d'Euler.[/b]
Algunes propietats dels centres d'un triangle

Més enllà dels quatre centres dels triangles

En el moment de preparar aquest material, aquesta enciclopèdia recull i classifica 16265 centres dels triangles . . . [url=http://faculty.evansville.edu/ck6/encyclopedia/ETC.html]http://faculty.evansville.edu/ck6/encyclopedia/ETC.html[/url][br]
[size=150][b]GoGeometry[/b][/size][br][br][img]https://cdn.geogebra.org/material/LCzl7Qhr9vOyzBmfAXJNwMIskrjSGH1f/material-lC8eSY6c.png[/img][br][br]Una font inesgotable de problemes de geometria[br]Mantinguda per Antonio Gutiérrez des del Perú[br][br][url=http://gogeometry.com/]http://gogeometry.com/[/url]

Més mates 2016

[i]Autor: Toni Gomà[/i][br][br]A partir d’un triangle (negre a la figura) dibuixem[br]tres quadrats A, B, C de manera que els[br]respectius costats són els costats del triangle. [br][br][img]data:image/png;base64,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[/img][br][br]Completem la figura amb tres triangles “exteriors”.[br][br]Feu conjectures sobre l’àrea d’aquests tres[br]triangles.[br][br]Relacioneu-les amb l’àrea del triangle inicial. [br][br]Sabríeu completar la figura perquè ens ajudi en la[br]demostració de la conjectura?[br][br]

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Més mates 2016

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