{"article_info":{"article_id":141176,"cat_id":1390,"cat_title":"SGK Toán 8 - Kết nối tri thức","publish_time":1686555960,"cat_id2":1390,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_35.png","title":"Giải bài 9.16 trang 92 SGK Toán 8 tập 2 - Kết nối tri thức ","label":"Giải bài 9.16 trang 92 ","alias":"giai-bai-916-trang-92-sgk-toan-8-tap-2-ket-noi-tri-thuc","introtext":"Cho hình thang ABCD ","content":"<style>\r\n.method-close-icon{position: relative;float: right;top: 6px;transform: rotate(270deg);-ms-transform:rotate(270deg);-moz-transform:rotate(270deg);-webkit-transform:rotate(270deg);-o-transform:rotate(270deg);}\r\n.method-open-icon{position: relative;float: right;top: 6px;}\r\n</style>\r\n<p><strong style=\"font-size: 16px;\">Đề bài</strong></p><p><span>Cho hình thang ABCD (AB // CD) và các điểm M, N lần lượt trên cạnh AD và BC sao cho </span><span class=\"mn\"><span>2</span></span><span class=\"mi\"><span>AM</span></span><span class=\"mo\"><span>=</span></span><span class=\"mi\"><span>MD</span></span><span>, </span><span class=\"mn\"><span>2</span></span><span class=\"mi\"><span>BN</span></span><span class=\"mo\"><span>=</span></span><span class=\"mi\"><span>NC</span></span><span>. Biết </span><span class=\"mi\"><span>AB</span></span><span class=\"mo\"><span>=</span></span><span class=\"mn\"><span>5</span></span><span class=\"mi\"><span>cm</span></span><span class=\"mo\"><span>,</span></span><span class=\"mi\"><span>CD</span></span><span class=\"mo\"><span>=</span></span><span class=\"mn\"><span>6</span></span><span class=\"mi\"><span>cm</span></span><span>. Hãy tính độ dài đoạn thẳng MN</span><strong></strong></p><div id=\"pos_end_question\"></div><div style=\"padding-top: 10px;padding-bottom: 2px;margin-bottom: 10px;\"><p class=\"show-detail-method\" style=\"background: #654bc2;text-align: center;border-radius:5px;padding: 10px;margin-bottom: 0px;\" onclick=\"showDetailMethod();\"><strong style=\"font-size: 16px;\">Phương pháp giải - Xem chi tiết</strong><img class=\"method-open-icon\" id=\"method_colapse_icon\" src=\"data:image/png;base64,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\"></p>  <div class=\"content_method_content\" style=\"padding: 10px 10px 5px 10px;border: dashed 1px #654bc2;border-top:none;\"><p>Gọi I là giao điểm của AC và MN</p>\r\n<p>Sử dụng các tam giác đồng dạng để tính độ dài MI, IN. Từ đó tính độ dài đoạn MN.</p>  </div>\r\n<script type=\"text/javascript\">\r\n    var is_open =true;\r\n    function showDetailMethod(){\r\n        if(is_open){\r\n            document.querySelector(\".content_method_content\").style.display='none';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-open-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-close-icon\");\r\n        }else{\r\n            document.querySelector(\".content_method_content\").style.display='block';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-close-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-open-icon\");\r\n        }\r\n        is_open = !is_open;\r\n    }\r\n</script>\r\n</div><p><strong style=\"font-size: 16px;\">Lời giải chi tiết</strong></p><p>Gọi I là giao điểm của AC và MN</p>\r\n<p><img src=\"https://img.loigiaihay.com/picture/2023/0612/1_45.png\" /></p>\r\n<p>Vì <span class=\"mn\"><span>2</span></span><span class=\"mi\"><span>AM</span></span><span class=\"mo\"><span>=</span></span><span class=\"mi\"><span>MD suy ra </span></span><span class=\"MTConvertedEquation\">\\(\\frac{{AM}}{{M{\\rm{D}}}} = \\frac{1}{2} \\Rightarrow \\frac{{AM}}{{A{\\rm{D}}}} = \\frac{1}{3}\\)</span></p>\r\n<p><span class=\"mi\"><span>Vì </span></span><span class=\"mn\"><span>2</span></span><span class=\"mi\"><span>BN</span></span><span class=\"mo\"><span>=</span></span><span class=\"mi\"><span>NC suy ra </span></span><span class=\"MTConvertedEquation\">\\(\\frac{{BN}}{{NC}} = \\frac{1}{2} \\Rightarrow \\frac{{NC}}{{CB}} = \\frac{2}{3}\\)</span></p>\r\n<p><span class=\"mi\"><span>Xét hình thang ABCD có </span></span><span class=\"MTConvertedEquation\">\\(\\frac{{AM}}{{M{\\rm{D}}}} = \\frac{{BN}}{{NC}}\\)</span><span class=\"mi\"><span> suy ra MN // AB //DC</span></span></p>\r\n<p><span class=\"mi\"><span>Xét hai tam giác AMI và ADC có: góc A chung, </span></span><span class=\"MTConvertedEquation\">\\(\\widehat {AIM} = \\widehat {AC{\\rm{D}}}\\)</span><span class=\"mi\"><span> (do MN// DC)</span></span></p>\r\n<p><span class=\"mi\"><span>Suy ra </span></span><span class=\"MTConvertedEquation\">\\(\\Delta AMI \\backsim \\Delta A{\\rm{D}}C\\)</span><span class=\"mi\"><span> suy ra: </span></span><span class=\"MTConvertedEquation\">\\(\\frac{{AM}}{{{\\rm{AD}}}} = \\frac{{MI}}{{DC}} = \\frac{1}{3} \\Rightarrow MI = \\frac{1}{3}.DC = \\frac{1}{3}.6 = 2(cm)\\)</span></p>\r\n<p><span class=\"mi\"><span>Xét hai tam giác CNI và CBA có góc C chung, </span></span><span class=\"MTConvertedEquation\">\\(\\widehat {CIN} = \\widehat {CAB}\\)</span><span class=\"mi\"><span> (do MN // AB)</span></span></p>\r\n<p><span class=\"mi\"><span>Suy ra </span></span><span class=\"MTConvertedEquation\">\\(\\Delta CNI \\backsim \\Delta CBA\\) </span><span class=\"mi\"><span>suy ra: </span></span><span class=\"MTConvertedEquation\">\\(\\frac{{CN}}{{CB}} = \\frac{{NI}}{{BA}} = \\frac{2}{3} \\Rightarrow NI = \\frac{2}{3}.BA = \\frac{2}{3}.5 = \\frac{{10}}{3}\\)</span><span class=\"mi\"><span>(cm)</span></span></p>\r\n<p><span class=\"mi\"><span>MN = MI + IN = </span></span><span class=\"MTConvertedEquation\">\\(2 + \\frac{{10}}{3} = \\frac{{16}}{3}(cm)\\)</span></p>","common_article":"","display_type":1,"vungoi_exam_id":"","article_type":1,"cmt_count":0,"zip_status":1,"last_modified_time":1707959316,"last_zip_time":1707959316,"zip_link":"https://offline.loigiaihay.com/articles/1390/141176/141176_1707959316.zip","picture":"https://img.loigiaihay.com/picture/article/2023/0612/1-0_35.png","youtube_id":"yNq0M4AC9C8","video_start_time":"1061","quizlet_id":"0","ref_article_id":0,"readmore_display_type":0,"wiki":0,"comment_url":"https://loigiaihay.com/comment/giai-bai-916-trang-92-sgk-toan-8-tap-2-ket-noi-tri-thuc-c1390a141176.html","origin_url":"https://loigiaihay.com/giai-bai-916-trang-92-sgk-toan-8-tap-2-ket-noi-tri-thuc-c1390a141176.html","relate_link":[],"exam_file":"","solution_file":""},"callouts":[],"relate_articles":[],"others_in_cat":[{"article_id":144107,"cat_id":1390,"publish_time":1689068820,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0711/resize_1-0_7.png","title":"Lý thuyết Định lí Pythagore và ứng dụng SGK Toán 8 - Kết nối tri thức","alias":"ly-thuyet-dinh-li-pythagore-va-ung-dung-sgk-toan-8-ket-noi-tri-thuc","introtext":"Định lí Pythagore là gì?","display_type":0,"article_type":1},{"article_id":141174,"cat_id":1390,"publish_time":1686555840,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_34.png","title":"Giải bài 9.15 trang 92 SGK Toán 8 tập 2 - Kết nối tri thức ","alias":"giai-bai-915-trang-92-sgk-toan-8-tap-2-ket-noi-tri-thuc","introtext":"Cho các điểm A, B, C, D, E như Hình 9.30. 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