{"id":18487,"date":"2024-11-07T09:46:30","date_gmt":"2024-11-07T08:46:30","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=18487"},"modified":"2024-11-07T11:54:19","modified_gmt":"2024-11-07T10:54:19","slug":"chapitre-4-agrandissement-et-reduction-dune-figure","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-4-agrandissement-et-reduction-dune-figure\/","title":{"rendered":"Chapitre 4 : Agrandissement et r\u00e9duction d&rsquo;une figure"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"18487\" class=\"elementor elementor-18487\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-621239b3 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"621239b3\" data-element_type=\"section\" 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elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6520a2ec elementor-widget elementor-widget-heading\" data-id=\"6520a2ec\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 4<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11dc166f elementor-widget elementor-widget-heading\" data-id=\"11dc166f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Agrandissement et r\u00e9duction<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5f7f33ed elementor-widget elementor-widget-text-editor\" data-id=\"5f7f33ed\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-1254bd5\" data-id=\"1254bd5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ece67f2 elementor-widget elementor-widget-image\" data-id=\"ece67f2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"192\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/cours-maths-4eme.png\" class=\"attachment-medium size-medium wp-image-15214\" alt=\"Cours de math\u00e9matiques de 4\u00e8me\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8d2f689 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d2f689\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7093303\" data-id=\"7093303\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-26855e1 elementor-widget elementor-widget-spacer\" data-id=\"26855e1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e19056e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e19056e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f5c44dc\" data-id=\"f5c44dc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b6dc547 elementor-widget elementor-widget-heading\" data-id=\"b6dc547\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 4 : Agrandissement et r\u00e9duction<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0ac6cbb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0ac6cbb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c30590c\" data-id=\"c30590c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-814d9e9 elementor-widget elementor-widget-spacer\" data-id=\"814d9e9\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d87d477 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d87d477\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d470437\" data-id=\"d470437\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-24eed88 elementor-widget elementor-widget-heading\" data-id=\"24eed88\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">A) Agrandissement et r\u00e9duction d'une figure<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-018f1fe elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"018f1fe\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bca02f1\" data-id=\"bca02f1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eae7b0a elementor-widget elementor-widget-text-editor\" data-id=\"eae7b0a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9finition :<\/strong> Faire un <strong>agrandissement<\/strong> d&rsquo;une figure c&rsquo;est multiplier toutes les longueurs par un m\u00eame nombre $k$ sup\u00e9rieur \u00e0 1 en conservant la forme de la figure.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bc987f7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bc987f7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-26cb025\" data-id=\"26cb025\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4ab3124 elementor-widget elementor-widget-text-editor\" data-id=\"4ab3124\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Vocabulaire :<\/strong> $k$ est appel\u00e9 le <strong>rapport d&rsquo;agrandissement<\/strong>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8943744 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8943744\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4139030\" data-id=\"4139030\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-57c0c46 elementor-widget elementor-widget-text-editor\" data-id=\"57c0c46\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le triangle $A&rsquo;B&rsquo;C&rsquo;$ est un agrandissement du triangle $ABC$. Les longueurs ont \u00e9t\u00e9 multipli\u00e9es par 1,5. En effet :<br \/>\\[3\\times 1,5=4,5~~~~4\\times 1,5=6~~~~5\\times 1,5=7,5\\]<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18500 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/agrandissement.png\" alt=\"agrandissement d'une figure\" width=\"682\" height=\"299\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/agrandissement.png 682w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/agrandissement-300x132.png 300w\" sizes=\"auto, (max-width: 682px) 100vw, 682px\" \/><\/p><p>Les dimensions de la figure obtenue lors d&rsquo;un agrandissement sont proportionnelles \u00e0 celles de la figure initiale.<br \/>\\[\\dfrac{4,5}{3}=\\dfrac{6}{4}=\\dfrac{7,5}{5}=\\textcolor{red}{1,5}\\]<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18502 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-agrandissement.png\" alt=\"tableau de proportionnalit\u00e9\" width=\"589\" height=\"65\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-agrandissement.png 589w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-agrandissement-300x33.png 300w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fb936d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fb936d0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bda542d\" data-id=\"bda542d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-17e8a4a elementor-widget elementor-widget-text-editor\" data-id=\"17e8a4a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9finition :<\/strong> Faire une <strong>r\u00e9duction<\/strong> d&rsquo;une figure c&rsquo;est multiplier toutes les longueurs par un m\u00eame nombre $k$ compris entre 0 et 1 en conservant la forme de la figure.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-450b2a5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"450b2a5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-eb9cc46\" data-id=\"eb9cc46\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bdb43ba elementor-widget elementor-widget-text-editor\" data-id=\"bdb43ba\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Vocabulaire :<\/strong> $k$ est appel\u00e9 le<strong> rapport de r\u00e9duction<\/strong>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-87c8f70 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"87c8f70\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ba11051\" data-id=\"ba11051\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-936e1ad elementor-widget elementor-widget-text-editor\" data-id=\"936e1ad\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le triangle $A&rsquo;B&rsquo;C&rsquo;$ est une r\u00e9duction du triangle $ABC$. Les longueurs ont \u00e9t\u00e9 multipli\u00e9es par 0,5. En effet :<br \/>\\[4\\times 0,5=2~~~~6\\times 0,5=3~~~~8\\times 0,5=4\\]<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18501 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/reduction.png\" alt=\"r\u00e9duction d'une figure\" width=\"652\" height=\"280\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/reduction.png 652w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/reduction-300x129.png 300w\" sizes=\"auto, (max-width: 652px) 100vw, 652px\" \/><\/p><p>Les dimensions de la figure obtenue lors d&rsquo;une r\u00e9duction sont proportionnelles \u00e0 celles de la figure initiale.<br \/>\\[\\dfrac{2}{4}=\\dfrac{3}{6}=\\dfrac{4}{8}=\\textcolor{red}{0,5}\\]<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18503 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-reduction.png\" alt=\"tableau de proportionnalit\u00e9\" width=\"568\" height=\"82\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-reduction.png 568w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/tableau-reduction-300x43.png 300w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-517624d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"517624d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ab121ee\" data-id=\"ab121ee\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a5719ee elementor-widget elementor-widget-spacer\" data-id=\"a5719ee\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-41c8067 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"41c8067\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a7ed4c5\" data-id=\"a7ed4c5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-53cc90e elementor-widget elementor-widget-heading\" data-id=\"53cc90e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">B) Conservation des angles et du parall\u00e9lisme<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-10ee50d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"10ee50d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-79d8d62\" data-id=\"79d8d62\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6b2781c elementor-widget elementor-widget-text-editor\" data-id=\"6b2781c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Cons\u00e9quence :<\/strong> Lors de l&rsquo;agrandissement ou de la r\u00e9duction d&rsquo;une figure :<\/p><ul><li>les mesures des angles sont conserv\u00e9es (donc la perpendicularit\u00e9 en particulier) ;<\/li><li>le parall\u00e9lisme est conserv\u00e9.<br \/><br \/><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d64a8c8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d64a8c8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ee29224\" data-id=\"ee29224\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-94ee51f elementor-widget elementor-widget-text-editor\" data-id=\"94ee51f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Le triangle $A&rsquo;B\u2019C\u2019$ est un agrandissement du triangle $ABC$ dans le rapport 2. Donc :<\/p><p>\\[ C&rsquo;B&rsquo;=2\\times CB\\]\\[\\widehat{ACB}=\\widehat{A&rsquo;B&rsquo;C&rsquo;}\\]<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18510 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/conservation-angle.png\" alt=\"Conservation de la mesure des angles lors d'un agrandissement.\" width=\"532\" height=\"356\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/conservation-angle.png 532w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/conservation-angle-300x201.png 300w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-068a250 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"068a250\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-82cd68e\" data-id=\"82cd68e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0fc59ba elementor-widget elementor-widget-spacer\" data-id=\"0fc59ba\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-25af141 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"25af141\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-77b458f\" data-id=\"77b458f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4933a5f elementor-widget elementor-widget-heading\" data-id=\"4933a5f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">C) Effet sur les aires<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-873c80d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"873c80d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-19f73b7\" data-id=\"19f73b7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1473d03 elementor-widget elementor-widget-text-editor\" data-id=\"1473d03\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> Si les longueurs d&rsquo;une figure sont multipli\u00e9es par un nombre $k$ (positif), alors l&rsquo;aire est multipli\u00e9e par $k^{2}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-faebc38 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"faebc38\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-727df69\" data-id=\"727df69\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-52a2f0c elementor-widget elementor-widget-text-editor\" data-id=\"52a2f0c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le rectangle $A&rsquo;B&rsquo;C&rsquo;D&rsquo;$ est un agrandissement du rectangle $ABCD$ de coefficient 3.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18517 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-aire.png\" alt=\"Effet sur les aires d'un agrandissement.\" width=\"664\" height=\"268\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-aire.png 664w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-aire-300x121.png 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><br \/>Or :<br \/>$A_{ABCD}=1~\\text{cm}\\times 2~\\text{cm}=2~\\text{cm}^{2}$<\/p><p>$A_{A&rsquo;B&rsquo;C&rsquo;D&rsquo;}=3~\\text{cm}\\times 6~\\text{cm}=18~\\text{cm}^{2}$<\/p><p>L&rsquo;aire a \u00e9t\u00e9 multipli\u00e9e par $3^{2}=9$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8a3a11c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8a3a11c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-424c1db\" data-id=\"424c1db\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b2bba80 elementor-widget elementor-widget-text-editor\" data-id=\"b2bba80\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> La surface d&rsquo;un champ est de 12 hectares. On multiplie ses dimensions par 2,5. Quelle sera sa nouvelle surface?<br \/>\\begin{eqnarray*}<br \/>A_{nouvelle~surface}&amp;=&amp;2,5^{2}\\times A_{surface~de~d\u00e9part}\\\\<br \/>&amp;=&amp;2,5^{2}\\times 12~\\text{hectares}\\\\<br \/>&amp;=&amp;75~\\text{hectares}<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ec9a6a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ec9a6a7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1e400dd\" data-id=\"1e400dd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b8fa786 elementor-widget elementor-widget-spacer\" data-id=\"b8fa786\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9d24ea0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9d24ea0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1624f7c\" data-id=\"1624f7c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-645ac81 elementor-widget elementor-widget-heading\" data-id=\"645ac81\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">D) Effet sur les volumes<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-45d998d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"45d998d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-08df702\" data-id=\"08df702\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7ea6217 elementor-widget elementor-widget-text-editor\" data-id=\"7ea6217\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9 :<\/strong> Si les longueurs d&rsquo;une figure sont multipli\u00e9es par un nombre $k$ (positif), alors le volume est multipli\u00e9 par $k^{3}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-60c8222 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"60c8222\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-98d4692\" data-id=\"98d4692\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f4ffcee elementor-widget elementor-widget-text-editor\" data-id=\"f4ffcee\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Sur la figure ci-dessous, le 2\u00e8me pav\u00e9 droit est un agrandissement du 1er pav\u00e9 droit de coefficient 2.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18518 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-volume.png\" alt=\"Effet sur les volumes d'un agrandissement.\" width=\"554\" height=\"302\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-volume.png 554w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/11\/effet-volume-300x164.png 300w\" sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><\/p><p>Or :<br \/>$V_{pav\u00e9~droit~1}=1~\\text{cm}\\times 1~\\text{cm}\\times 2~\\text{cm}=2~\\text{cm}^{3}$<\/p><p>$V_{pav\u00e9~droit~2}=2~\\text{cm}\\times 2~\\text{cm}\\times 4~\\text{cm}=16~\\text{cm}^{3}$<\/p><p>Le volume a \u00e9t\u00e9 multipli\u00e9 par $2^{3}=8$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bea7d3e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bea7d3e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ededcda\" data-id=\"ededcda\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e49dbb9 elementor-widget elementor-widget-spacer\" data-id=\"e49dbb9\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4602724 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4602724\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bf4e93f\" data-id=\"bf4e93f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d9ceadd elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"d9ceadd\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/NoEjwSkZQQSfskH\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-074673e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"074673e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-41f1527\" data-id=\"41f1527\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bfdf283 elementor-widget elementor-widget-spacer\" data-id=\"bfdf283\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 4 Agrandissement et r\u00e9duction Chapitre 4 : Agrandissement et r\u00e9duction A) Agrandissement et r\u00e9duction d&rsquo;une figure D\u00e9finition : Faire un agrandissement d&rsquo;une figure c&rsquo;est multiplier toutes les longueurs par un m\u00eame nombre $k$ sup\u00e9rieur \u00e0 1 en conservant la forme de la figure. Vocabulaire : $k$ est appel\u00e9 le rapport d&rsquo;agrandissement. Exemple : Sur [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":18564,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"unboxed","site-sidebar-style":"unboxed","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[43],"tags":[],"class_list":["post-18487","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cours-et-exercices-3eme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - 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