{"id":15673,"date":"2023-02-07T21:27:17","date_gmt":"2023-02-07T20:27:17","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=15673"},"modified":"2025-12-22T08:37:35","modified_gmt":"2025-12-22T07:37:35","slug":"chapitre-8-la-reciproque-du-theoreme-de-pythagore","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-8-la-reciproque-du-theoreme-de-pythagore\/","title":{"rendered":"Chapitre 8 : La r\u00e9ciproque du th\u00e9or\u00e8me de Pythagore"},"content":{"rendered":"\t\t
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Chapitre 8<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Chapitre 8 : R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore<\/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
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Propri\u00e9t\u00e9 (R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore) :<\/strong> Si le carr\u00e9 de la longueur du plus grand c\u00f4t\u00e9 d\u2019un triangle est \u00e9gal \u00e0 la somme des carr\u00e9s des longueurs des deux autres c\u00f4t\u00e9s, alors ce triangle est rectangle.<\/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

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Remarque :<\/strong> Cette propri\u00e9t\u00e9 permet de prouver qu\u2019un triangle est rectangle ou non.<\/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

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Exemple :<\/strong> Le triangle $I JK$ est-il rectangle ?<\/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

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$$
\\left.
\\begin{array}
~IK^{2}=17^{2}=289 \\\\
IJ^{2}+JK^{2}=8^{2}+15^{2}=64+225=289
\\end{array}
\\right \\} ~\\text{Donc}~IK^{2}=IJ^{2}+JK^{2}
$$<\/p>

Ainsi, l’\u00e9galit\u00e9 de Pythagore est v\u00e9rifi\u00e9e donc le triangle $IJK$ est rectangle en $J$.<\/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

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Propri\u00e9t\u00e9 :<\/strong> Si le carr\u00e9 de la longueur du plus grand c\u00f4t\u00e9 d\u2019un triangle n\u2019est pas \u00e9gal \u00e0 la somme des carr\u00e9s des longueurs des deux autres c\u00f4t\u00e9s, alors ce triangle n\u2019est pas rectangle.<\/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

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Exemple :<\/strong> Le triangle $ABC$ est-il rectangle ?<\/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

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$$
\\left.
\\begin{array}
~AC^{2}=6^{2}=36 \\\\
AB^{2}+BC^{2}=5^{2}+3^{2}=25+9=34
\\end{array}
\\right \\} ~\\text{Donc}~AC^{2}\\neq AB^{2}+BC^{2}
$$<\/p>

Ainsi, l’\u00e9galit\u00e9 de Pythagore n’est pas v\u00e9rifi\u00e9e donc le triangle $ABC$ n’est pas rectangle en $B$.<\/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

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Chapitre 8 R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore Chapitre 8 : R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore Propri\u00e9t\u00e9 (R\u00e9ciproque du th\u00e9or\u00e8me de Pythagore) : Si le carr\u00e9 de la longueur du plus grand c\u00f4t\u00e9 d\u2019un triangle est \u00e9gal \u00e0 la somme des carr\u00e9s des longueurs des deux autres c\u00f4t\u00e9s, alors ce triangle est rectangle. Remarque : Cette […]<\/p>\n","protected":false},"author":7440,"featured_media":16068,"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":"page-builder","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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