{"id":85,"date":"2023-07-06T11:36:43","date_gmt":"2023-07-06T11:36:43","guid":{"rendered":"https:\/\/el-raconet.com\/?p=85"},"modified":"2026-03-25T11:29:09","modified_gmt":"2026-03-25T09:29:09","slug":"els-poligons-que-son-i-com-es-classifiquen","status":"publish","type":"post","link":"https:\/\/el-raconet.com\/index.php\/2023\/07\/06\/els-poligons-que-son-i-com-es-classifiquen\/","title":{"rendered":"Els pol\u00edgons, qu\u00e8 s\u00f3n i com es classifiquen"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Que s\u00f3n els pol\u00edgons?<\/h2>\n\n\n\n<p>Els <strong>pol\u00edgons<\/strong> s\u00f3n figures geom\u00e8triques planes formades per l\u00ednies poligonals tancades. S\u00f3n figures en dues dimensions, per tant, nom\u00e9s poden existir en un <strong>pla<\/strong> (superf\u00edcie imagin\u00e0ria infinita i sense curvatura). <\/p>\n\n\n\n<p>Les parts m\u00e9s importants que caracteritzen un pol\u00edgon s\u00f3n les seg\u00fcents:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Costats:<\/strong> Segments que limiten el pol\u00edgon.<\/li>\n\n\n\n<li><strong>V\u00e8rtex:<\/strong> \u00c9s el punt on convergeixen dos costats.<\/li>\n\n\n\n<li><strong>Angle:<\/strong> \u00c9s l&#8217;obertura que formen dos costats amb el seu v\u00e8rtex. Es mesura en graus.<\/li>\n\n\n\n<li><strong>Diagonal:<\/strong> Segment que uneix dos costats no consecutius.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"400\" src=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/vertex-500-\u00d7-400-px.png\" alt=\"Les parts d'un pol\u00edgon\" class=\"wp-image-91\" style=\"width:258px;height:206px\" title=\"Les parts d'un pol\u00edgon\" srcset=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/vertex-500-\u00d7-400-px.png 500w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/vertex-500-\u00d7-400-px-300x240.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Hi ha moltes formes de classificar els <strong>pol\u00edgons<\/strong>; segons nombre de costats, c\u00f2ncaus i convexos, regulars o irregulars&#8230;<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"dc-poligons-box\">\n  <div class=\"dc-poligons-box-title\">Material per treballar els pol\u00edgons a l\u2019aula<\/div>\n  <p>\n    Si vols portar aquests conceptes a la pr\u00e0ctica, aquest material inclou activitats de classificaci\u00f3, per\u00edmetre i \u00e0rea pensades per a prim\u00e0ria.\n  <\/p>\n  <a href=\"https:\/\/docenciacompartida.com\/downloads\/aprenem-els-poligons-pas-a-pas\/\" class=\"dc-poligons-box-link\">\n    \u2192 Aprenem els pol\u00edgons pas a pas\n  <\/a>\n<\/div>\n\n\n\n<p>A continuaci\u00f3 veurem algunes d&#8217;aquestes formes de classificaci\u00f3.<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Pol\u00edgons regulars i irregulars<\/h2>\n\n\n\n<p>Un <strong>pol\u00edgon regular<\/strong> \u00e9s aquell que t\u00e9 tots els <strong>costats<\/strong> i <strong>angles<\/strong> iguals. Aix\u00f2 significa que tots els costats tenen la mateixa <strong>longitud<\/strong> i tots els angles tenen la mateixa <strong>mesura<\/strong>. Els pol\u00edgons regulars s\u00f3n altament sim\u00e8trics i tenen patrons repetitius. Alguns exemples de pol\u00edgons regulars s\u00f3n el <strong>quadrat<\/strong>, l&#8217;<strong>hex\u00e0gon regular<\/strong> i el <strong>triangle equil\u00e0ter<\/strong>. Aquests pol\u00edgons regulars tenen propietats ben definides i s\u00f3n f\u00e0cilment reconeixibles per la seva <strong>simetria<\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"250\" src=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-250-px.png\" alt=\"Pol\u00edgons regulars\" class=\"wp-image-90\" style=\"width:504px;height:180px\" title=\"Pol\u00edgons regulars\" srcset=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-250-px.png 700w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-250-px-600x214.png 600w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-250-px-300x107.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure><\/div>\n\n\n<p>En canvi, un <strong>pol\u00edgon irregular<\/strong> \u00e9s aquell que t\u00e9 costats i angles de longituds i mesures <strong>diferents<\/strong>. No segueix cap patr\u00f3 espec\u00edfic i pot tenir costats de longituds diferents i angles de mesures diverses.  Alguns exemples de pol\u00edgons irregulars s\u00f3n el <strong>rectangle<\/strong>, el <strong>rombe<\/strong>, el triangle <strong>is\u00f2sceles<\/strong>&#8230;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"300\" src=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-300-px.png\" alt=\"Pol\u00edgons irregulars\" class=\"wp-image-89\" style=\"width:528px;height:226px\" title=\"Pol\u00edgons irregulars\" srcset=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-300-px.png 700w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-300-px-600x257.png 600w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Quadrat-700-\u00d7-300-px-300x129.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure><\/div>\n\n\n<p>Els pol\u00edgons irregulars s\u00f3n m\u00e9s variats i no tenen les mateixes propietats sim\u00e8triques que els pol\u00edgons regulars.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Classificaci\u00f3 segons costats<\/h2>\n\n\n\n<p>Una altra manera de classificar els pol\u00edgons \u00e9s segons el nombre de costats que tenen:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Triangle<\/strong>: Un pol\u00edgon de <strong>tres<\/strong> costats.<\/li>\n\n\n\n<li><strong>Quadril\u00e0ter<\/strong>: Un pol\u00edgon de <strong>quatre<\/strong> costats.<\/li>\n\n\n\n<li><strong>Pent\u00e0gon<\/strong>: Un pol\u00edgon de <strong>cinc<\/strong> costats.<\/li>\n\n\n\n<li><strong>Hex\u00e0gon<\/strong>: Un pol\u00edgon de <strong>sis<\/strong> costats.<\/li>\n\n\n\n<li><strong>Hept\u00e0gon<\/strong>: Un pol\u00edgon de <strong>set<\/strong> costats.<\/li>\n\n\n\n<li><strong>Oct\u00e0gon:<\/strong> Un pol\u00edgon de <strong>vuit <\/strong>costats.<\/li>\n\n\n\n<li><strong>Enne\u00e0gon<\/strong>: Un pol\u00edgon de <strong>nou<\/strong> costats.<\/li>\n\n\n\n<li><strong>Dec\u00e0gon<\/strong>: Un pol\u00edgon de <strong>deu<\/strong> costats.<\/li>\n\n\n\n<li><strong>Hendec\u00e0gon<\/strong>: Un pol\u00edgon d&#8217;<strong>onze<\/strong> costats.<\/li>\n\n\n\n<li><strong>Dodec\u00e0gon<\/strong>: Un pol\u00edgon de <strong>dotze<\/strong> costats.<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"441\" src=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-1024x441.jpg\" alt=\"Pol\u00edgons segons costats\" class=\"wp-image-92\" style=\"width:510px;height:219px\" title=\"Pol\u00edgons segons costats\" srcset=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-1024x441.jpg 1024w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-scaled-600x259.jpg 600w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-300x129.jpg 300w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-768x331.jpg 768w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-1536x662.jpg 1536w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/Els-poligons-2-2048x882.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">Convexos i c\u00f2ncaus<\/h2>\n\n\n\n<p>Un pol\u00edgon <strong>convex<\/strong> \u00e9s aquell en qu\u00e8 tots els angles interiors mesuren <strong>menys<\/strong> de 180 graus. En altres paraules, totes les diagonals que es poden tra\u00e7ar, es troben <strong>dins<\/strong> de la superf\u00edcie del pol\u00edgon.<\/p>\n\n\n\n<p>Un pol\u00edgon no convex o <strong>c\u00f2ncau<\/strong>, \u00e9s aquell que t\u00e9 almenys un angle interior <strong>m\u00e9s gran<\/strong> de 180 graus. Quan es dona aquesta situaci\u00f3, alguna de les diagonals que es poden tra\u00e7ar, es trobaran a l&#8217;<strong>exterior<\/strong> de la superf\u00edcie del pol\u00edgon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"450\" src=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/convex.png\" alt=\"\" class=\"wp-image-94\" style=\"width:373px;height:240px\" srcset=\"https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/convex.png 700w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/convex-600x386.png 600w, https:\/\/el-raconet.com\/wp-content\/uploads\/2023\/07\/convex-300x193.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure><\/div>\n\n\n<div class=\"dc-poligons-box\">\n  <div class=\"dc-poligons-box-title\">Vols portar-ho a la pr\u00e0ctica?<\/div>\n  <p>\n    Si despr\u00e9s d\u2019entendre la teoria vols que l\u2019alumnat practiqui, aquest material inclou m\u00e9s de 25 activitats progressives per treballar els pol\u00edgons, el per\u00edmetre i l\u2019\u00e0rea a prim\u00e0ria.\n  <\/p>\n  <a href=\"https:\/\/docenciacompartida.com\/downloads\/aprenem-els-poligons-pas-a-pas\/\" class=\"dc-poligons-box-link\">\n    \u2192 Veure activitats de pol\u00edgons per prim\u00e0ria (PDF)\n  <\/a>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">V\u00eddeo resum<\/h2>\n\n\n\n<p>A continuaci\u00f3 teniu un v\u00eddeo amb el resum de les caracter\u00edstiques dels pol\u00edgons que s&#8217;han esmentat anteriorment. A m\u00e9s, al final del v\u00eddeo, hi ha unes activitats per practicar. Endavant!<\/p>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"ELS POL\u00cdGONS | Espai i forma\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/VtWCsHcIiuM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>El pol\u00edgons s\u00f3n figures geom\u00e8triques formades per l\u00ednies poligonals. Es poden classificar de moltes maneres diferents&#8230;<\/p>\n","protected":false},"author":1,"featured_media":333,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[10,11,5,6],"class_list":["post-85","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geometria","tag-eso","tag-geometria","tag-matematiques","tag-primaria"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/posts\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/comments?post=85"}],"version-history":[{"count":5,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/posts\/85\/revisions"}],"predecessor-version":[{"id":1533,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/posts\/85\/revisions\/1533"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/media\/333"}],"wp:attachment":[{"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/media?parent=85"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/categories?post=85"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/el-raconet.com\/index.php\/wp-json\/wp\/v2\/tags?post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}