{"id":2435,"date":"2020-10-14T17:46:38","date_gmt":"2020-10-14T09:46:38","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=2435"},"modified":"2020-11-02T14:46:41","modified_gmt":"2020-11-02T06:46:41","slug":"geometry-similar-triangles","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry-similar-triangles\/","title":{"rendered":"12. \u6f14\u7e79\u63a8\u7406\u5e7e\u4f55 > \u76f8\u4f3c\u4e09\u89d2\u5f62"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2435\" class=\"elementor elementor-2435\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-33d4fb3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"33d4fb3\" data-element_type=\"section\" data-e-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-66 elementor-top-column elementor-element elementor-element-ba1e617\" data-id=\"ba1e617\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-234efac elementor-widget elementor-widget-text-editor\" data-id=\"234efac\" data-element_type=\"widget\" data-e-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<h2>12.5.\u00a0 \u76f8\u4f3c\u4e09\u89d2\u5f62 (Similar Triangles)<\/h2><p>\u8b1b \u76f8\u4f3c\u4e09\u89d2\u5f62 \uff0c\u9996\u5148\u7576\u7136\u8981\u8b1b\u5413\u500b\u5b9a\u7fa9\u2026<\/p><ul><li><strong>\u76f8\u4f3c<\/strong>\u00a0<ul><li>\u6307\u5169\u500b\u5716\u5f62\u5605\u5f62\u72c0\u76f8\u540c\u3002<\/li><li>\u4e00\u500b\u5716\u5f62\u7d93\u653e\u5927\u6216\u7e2e\u5c0f\u8b8a\u63db\u5f8c\uff0c\u53ef\u7522\u751f\u4e00\u500b\u8207\u539f\u4f86\u5716\u5f62\u76f8\u4f3c\u5605\u5716\u5f62\u3002<\/li><\/ul><\/li><\/ul><p>\u76f8\u4f3c \u5605\u7b26\u865f\u4fc2 \\(\\sim\\)<\/p><ul><li>\\(\\triangle ABC \u8207 \\triangle XYZ \u76f8\u4f3c \u53ef\u5beb\u6210 \\triangle ABC \\sim \\triangle XYZ \\)<br \/>\uff08\u7559\u610f\u4e00\u5b9a\u8981\u8ddf\u5c0d\u61c9\u89d2\u5605\u4f4d\u7f6e\u5beb\u51fa\u25b3\u7684\u540d\u5b57\uff09<\/li><\/ul><p>\u00a0<\/p><h3>12.5.1 \u76f8\u4f3c\u4e09\u89d2\u5f62\u6027\u8cea<\/h3><p>\u7576\u5169\u500b\u25b3\u4fc2\u76f8\u4f3c\u6642\uff0c\u5982 \\(\\triangle ABC \\sim \\triangle XYZ \\)<\/p><ul><li>\u4f62\u54cb\u5605\u5c0d\u61c9\u89d2\u76f8\u7b49<br \/>\u00a0\\(\\angle A =\\angle X\uff0c \\angle B = \\angle Y\uff0c\\angle C = \\angle Z \\) <\/li><li>\u4f62\u54cb\u5605\u5c0d\u61c9\u908a\u5605\u6bd4\u4f8b\u76f8\u7b49 (corresponding sides are proportional) <br \/>\\(\\dfrac{AB}{XY} = \\dfrac{BC}{YZ} = \\dfrac{CA}{ZX} \\)<\/li><\/ul><p>\u00a0<\/p><h3>12.5.2\u00a0 \u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u689d\u4ef6<\/h3><p>\u660e\u767d\u5497\u4e0a\u9762\u5605\u57fa\u672c\u5622\u4e4b\u5f8c\uff0c\u66f4\u52a0\u7dca\u8981\u5605\u4fc2\u77e5\u9053\u5e7e\u6642\u5169\u500b\u4e09\u89d2\u5f62\u5148\u4fc2\u76f8\u4f3c\u3002\u4e0b\u9762\u5e45\u5716\u5df2\u7e3d\u7d50\u5497\u76f8\u4f3c\u5605\u689d\u4ef6\uff1a<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-1106\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_similarTriangleCond.jpg\" alt=\"\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u689d\u4ef6\" width=\"609\" height=\"167\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_similarTriangleCond.jpg 609w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_similarTriangleCond-300x82.jpg 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><\/p><p>\u00a0<\/p><h3>12.5.3.\u00a0 \u516c\u958b\u8a66\u63d0\u9ede<\/h3><ul><li>\u76f8\u4f3c\u4e09\u89d2\u5f62 \u8003\u5f97\u591a\u904e \u5168\u7b49\u4e09\u89d2\u5f62\u3002<ul><li>\u4f9d\u500b\u4fc2\u56e0\u70ba\u76f8\u4f3c\u76f8\u4f3c\u4e09\u89d2\u5f62\u5605\u984c\u76ee\u53ef\u4ee5\u9023\u57cb\u201c\u76f8\u4f3c\u5716\u5f62\u7684\u9762\u7a4d\u53ca\u9ad4\u7a4d\u201d\u569f\u8003\u3002\u5373\u8981\u6c42\u4f60\u7747\u5230\u908a\u5169\u500b\u25b3\u76f8\u4f3c\uff0c\u7136\u5f8c\u5229\u7528\u201c\u76f8\u4f3c\u25b3\u7279\u6027\u201d\u4e2d\u5605\u908a\u9577\u6bd4\u569f\u6c42\u5176\u4ed6\u908a\u6216\u8a08\u5169\u500b\u5716\u5f62\u5605\u9762\u7a4d\u6bd4\u3002<\/li><\/ul><\/li><li>\u5168\u7b49\u540c\u76f8\u4f3c\u4e09\u89d2\u5f62\u597d\u591a\u6642\u90fd\u4fc2\u8003\u201c\u8b49\u660e\u984c\u201d\uff08\u4f8b\u5982\u53eb\u4f60\u8b49\u660e \\(\\triangle ABC \\sim \\triangle XYZ \\)\uff09\u3002<ul><li>\u540c\u5b78\u4e00\u822c\u90fd\u89ba\u5f97\u4f9dD\u984c\u76ee\u6bd4\u8f03\u96e3\u3002<\/li><li>\u57fa\u65bc\u984c\u76ee\u53eb\u4f60\u5f97\u8b49\u660e\u5605\u5622\u4fc2\u4e00\u5b9a\u5571\uff0c\u8981\u505a\u5605\u5622\u4fc2\u5beb\u51fa\u9ede\u89e3\u6211\u54cb\u77e5\u9053\u4f62\u4fc2\u5571\u5c31\u5f97\u3002<\/li><\/ul><\/li><\/ul><p><a href=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/10\/dseGeometry_08.webp\"><img decoding=\"async\" class=\"alignright wp-image-2441\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/10\/dseGeometry_08.webp\" alt=\"\u76f8\u4f3c\u4e09\u89d2\u5f62-\u4f8b1\" width=\"200\" height=\"110\" \/><\/a>\u4f8b1\uff1a\u5728\u53f3\u5716\u4e2d\uff0c\u2220BAC =\u2220CDE\uff1b\u8b49\u660e\\(\\triangle ABC \\sim \\triangle DCE \\)<br \/>\u89e3\u8aaa\uff1a<\/p><ul><li>\u5148\u8981\u8ad7\u5413\u6709\u54a9\u65b9\u6cd5\u53ef\u4ee5\u8b49\u660e\u5169\u500b\u25b3\u76f8\u4f3c\uff0c\u518d\u7747\u5413\u53ef\u4ee5\u7528\u908a\u500b\u65b9\u6cd5\u3002<\/li><li>\u56e0\u70ba\u984c\u76ee\u5187\u63d0\u904e\u908a\u9577\uff0c\u6240\u4ee5\u53ef\u4ee5\u7528\u5605\u53ea\u6709 \u201c\u4e09\u89d2\u76f8\u7b49\u201d\u3002<ul><li>\u56e0\u6b64\u6211\u54cb\u8981\u5beb\u4f4e\u9ede\u89e3\u4e09\u96bb\u89d2\u76f8\u7b49<\/li><\/ul><\/li><\/ul><p>\u5beb\u6cd5\u5982\u4e0b\uff1a<\/p><p>\\(\\begin{align}<br \/>\\angle BAC &amp; = \\angle CDE\u00a0 \uff08\u5df2\u77e5\uff09\\quad \\quad {\\color{Red} \\leftarrow } \u4f9d\u884c\u8b1b\u9ede\u77e5\u9053\u7b2c\u4e00\u96bb\u89d2\u76f8\u7b49 \\\\<br \/>\\angle ACB &amp; = \\angle DEC\u00a0 \uff08\u540c\u4f4d\u89d2\uff0cAC\/\/DE\uff09\\quad \\quad {\\color{Red} \\leftarrow }\u4f9d\u884c\u8b1b\u9ede\u77e5\u7b2c\u4e8c\u96bb\u89d2\u76f8\u7b49 \\\\<br \/>\\angle ABC &amp; = \\angle DCE \uff08\u25b3\u5167\u89d2\u548c\uff09\\quad \\quad {\\color{Red} \\leftarrow }\u56e0\u5169\u500b\u25b3\u5df2\u6709\u5169\u96bb\u89d2\u76f8\u7b49\uff0c\u6240\u4ee5\u7b2c\u4e09\u96bb\u89d2\u90fd\u6703\u76f8\u7b49 \\\\<br \/>\\therefore \\quad \u00a0 \u25b3ABC &amp; \\sim \u25b3DCE\u00a0 \uff08\u4e09\u89d2\u76f8\u7b49\uff09 \\quad \\quad {\\color{Red} \\leftarrow }\u56e0\u4e09\u96bb\u89d2\u76f8\u7b49\uff0c\u6240\u4ee5\u53ef\u4ee5\u5beb\u51fa\u4f62\u54cb\u4fc2\u76f8\u4f3c\u5605 \\\\<br \/>\\end{align}\\)<\/p><p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-47d3284 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"47d3284\" data-element_type=\"section\" data-e-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-33 elementor-inner-column elementor-element elementor-element-d39ee48\" data-id=\"d39ee48\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c8e3834 elementor-widget elementor-widget-text-editor\" data-id=\"c8e3834\" data-element_type=\"widget\" data-e-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<a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry-congruent-triangles\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u5168\u7b49\u4e09\u89d2\u5f62<\/a>\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-33 elementor-inner-column elementor-element elementor-element-5905bc9\" data-id=\"5905bc9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-f0913cc\" data-id=\"f0913cc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-393cecc elementor-widget elementor-widget-text-editor\" data-id=\"393cecc\" data-element_type=\"widget\" data-e-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<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry-pythagorean-theorem\/\">\u7562\u6c0f\u5b9a\u7406 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\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<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a625898\" data-id=\"a625898\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-309f018 elementor-widget elementor-widget-sidebar\" data-id=\"309f018\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-5 > ul > li > a, .custom-menu-widget .ocean_custom_menu-5 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-5.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">DSE\u6578\u5b78 &#8211; \u5fc5\u4fee\u90e8\u5206\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-5 left dropdown-hover\"><ul id=\"menu-dsemaths_core\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1744\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1744\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/course-analysis\/\" class=\"menu-link\">\u8ab2\u7a0b\u5206\u6790 (Core)<\/a><\/li>\n<li  id=\"menu-item-1745\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children dropdown menu-item-1745\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/\" class=\"menu-link\">\u5514\u597d\u4ee5\u70ba\u5514\u99db\u8003 &#8211; \u76ee\u9304 <span class=\"nav-arrow fa fa-angle-down\"><\/span><\/a>\n<ul class=\"sub-menu\">\n\t<li  id=\"menu-item-4067\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4067\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/solving-equation\/\" class=\"menu-link\">1. \u89e3\u65b9\u7a0b<\/a><\/li>\n\t<li  id=\"menu-item-4068\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4068\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials\/\" class=\"menu-link\">2. \u591a\u9805\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4069\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4069\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/laws-of-indices\/\" class=\"menu-link\">3. \u6307\u6578\u5b9a\u5f8b<\/a><\/li>\n\t<li  id=\"menu-item-4070\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4070\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/factorization\/\" class=\"menu-link\">4. \u56e0\u5f0f\u5206\u89e3<\/a><\/li>\n\t<li  id=\"menu-item-4071\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4071\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/formulae\/\" class=\"menu-link\">5. \u516c\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4072\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4072\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/percentage\/\" class=\"menu-link\">6. \u767e\u5206\u6cd5<\/a><\/li>\n\t<li  id=\"menu-item-4073\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4073\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/rate-and-ratio\/\" class=\"menu-link\">7. \u7387\u53ca\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4074\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4074\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/functions\/\" class=\"menu-link\">8. \u51fd\u6578<\/a><\/li>\n\t<li  id=\"menu-item-4075\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4075\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/estimation\/\" class=\"menu-link\">9. \u4f30\u7b97<\/a><\/li>\n\t<li  id=\"menu-item-4076\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4076\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/inequalities\/\" class=\"menu-link\">10. \u4e0d\u7b49\u5f0f<\/a><\/li>\n\t<li  id=\"menu-item-4077\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4077\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/coordinates\/\" class=\"menu-link\">11. \u5750\u6a19<\/a><\/li>\n\t<li  id=\"menu-item-4079\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4079\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/geometry\/\" class=\"menu-link\">12. \u6f14\u7e79\u63a8\u7406\u5e7e\u4f55<\/a><\/li>\n\t<li  id=\"menu-item-4080\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4080\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/trigonometry\/\" class=\"menu-link\">13. \u4e09\u89d2\u6bd4<\/a><\/li>\n\t<li  id=\"menu-item-4081\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4081\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/shapes\/\" class=\"menu-link\">14. \u5e73\u9762\u53ca\u7acb\u9ad4\u5716\u5f62<\/a><\/li>\n\t<li  id=\"menu-item-4082\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4082\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/15-probability\/\" class=\"menu-link\">15. \u6982\u7387<\/a><\/li>\n\t<li  id=\"menu-item-4083\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-4083\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/16-statistics\/\" class=\"menu-link\">16. \u7d71\u8a08<\/a><\/li>\n<\/ul>\n<\/li>\n<li  id=\"menu-item-3231\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3231\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental_algebra\/\" class=\"menu-link\">\u57fa\u790e &#8211; \u6578\u8207\u4ee3\u6578<\/a><\/li>\n<li  id=\"menu-item-3241\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3241\"><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/fundamental-shape_n_space\/\" class=\"menu-link\">\u57fa\u790e &#8211; 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