{"article_info":{"article_id":141126,"cat_id":1391,"cat_title":"SGK Toán 8 - Chân trời sáng tạo","publish_time":1686537000,"cat_id2":1391,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_6.png","title":"Giải bài 4 trang 87 SGK Toán 8 tập 1– Chân trời sáng tạo","label":"Giải bài 4 trang 87 ","alias":"giai-bai-4-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao","introtext":"Cho tam giác ","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>Cho tam giác <span class=\"MTConvertedEquation\">\\(ABC\\)</span> vuông tại <span class=\"MTConvertedEquation\">\\(A\\)</span> (<span class=\"MTConvertedEquation\">\\(AB &lt; AC\\)</span>. Gọi <span class=\"MTConvertedEquation\">\\(D\\)</span> là trung điểm của <span class=\"MTConvertedEquation\">\\(BC\\)</span>. Vẽ <span class=\"MTConvertedEquation\">\\(DE\\)</span> // <span class=\"MTConvertedEquation\">\\(AB\\)</span>, vẽ <span class=\"MTConvertedEquation\">\\(DF\\)</span> // <span class=\"MTConvertedEquation\">\\(AC\\)</span> <span class=\"MTConvertedEquation\">\\((E \\in AC\\)</span>; <span class=\"MTConvertedEquation\">\\(F \\in AB)\\)</span>. Chứng minh rằng:</p>\r\n<p>a) Tứ giác <span class=\"MTConvertedEquation\">\\(AEDF\\)</span> là hình chữ nhật</p>\r\n<p>b) Tứ giác <span class=\"MTConvertedEquation\">\\(BFED\\)</span> là hình bình hành</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>a) Áp dụng dấu hiệu nhận biết hình chữ nhật</p>\r\n<p>b) Áp dụng dấu hiệu nhận biết hình bình hành</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><img src=\"https://img.loigiaihay.com/picture/2023/0612/1_22.png\" /></p>\r\n<p>a) Ta có:</p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\Delta ABC\\)</span> vuông tại <span class=\"MTConvertedEquation\">\\(A\\)</span> nên <span class=\"MTConvertedEquation\">\\(\\widehat {{\\rm{BAC}}} = 90^\\circ \\)</span> và <span class=\"MTConvertedEquation\">\\(AB \\bot AC\\)</span></p>\r\n<p>Mà <span class=\"MTConvertedEquation\">\\(DE\\)</span> // <span class=\"MTConvertedEquation\">\\(AB\\)</span> ; <span class=\"MTConvertedEquation\">\\(DF\\)</span> // <span class=\"MTConvertedEquation\">\\(AC\\)</span></p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(DE \\bot AC;\\;DF \\bot AB\\)</span></p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(\\widehat {DEA} = \\widehat {DFA} = 90^\\circ \\)</span></p>\r\n<p>Tứ giác <span class=\"MTConvertedEquation\">\\(AEDF\\)</span> có <span class=\"MTConvertedEquation\">\\(\\widehat {BAC} = \\widehat {DEA} = \\widehat {DFA} = 90^\\circ \\)</span> nên là hình chữ nhật</p>\r\n<p>b) Vì <span class=\"MTConvertedEquation\">\\(AEDF\\)</span> là hình chữ nhật (cmt)</p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(AE = DF\\)</span>; <span class=\"MTConvertedEquation\">\\(AF = DE\\)</span>; <span class=\"MTConvertedEquation\">\\(AF\\)</span> // <span class=\"MTConvertedEquation\">\\(DE\\)</span>; <span class=\"MTConvertedEquation\">\\(AE\\)</span> // <span class=\"MTConvertedEquation\">\\(DF\\)</span></p>\r\n<p>Vì <span class=\"MTConvertedEquation\">\\(DE \\bot AC;\\;DF \\bot AB\\)</span> (cmt)</p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(\\widehat {DEC} = \\widehat {BFD} = 90^\\circ \\)</span></p>\r\n<p>Xét <span class=\"MTConvertedEquation\">\\(\\Delta BFD\\)</span> và <span class=\"MTConvertedEquation\">\\(\\Delta DEC\\)</span> ta có:</p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\widehat {{\\rm{BFD}}} = \\widehat {{\\rm{DEC}}} = 90^\\circ \\)</span> (cmt)</p>\r\n<p><span class=\"MTConvertedEquation\">\\(BD = DC\\)</span> (gt)</p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\widehat {{\\rm{FBD}}} = \\widehat {{\\rm{EDC}}}\\)</span> (do <span class=\"MTConvertedEquation\">\\(DE\\)</span> // <span class=\"MTConvertedEquation\">\\(BF\\)</span> )</p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(\\Delta BFD = \\Delta DEC\\)</span> (ch – gn)</p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(BF = DE\\)</span>; <span class=\"MTConvertedEquation\">\\(DF = EC\\)</span> (hai cạnh tương tứng)</p>\r\n<p>Xét tứ giác <span class=\"MTConvertedEquation\">\\(BFED\\)</span> ta có:</p>\r\n<p><span class=\"MTConvertedEquation\">\\(BF\\)</span> // <span class=\"MTConvertedEquation\">\\(DE\\)</span> (do <span class=\"MTConvertedEquation\">\\(AB\\)</span> // <span class=\"MTConvertedEquation\">\\(DE\\)</span>)</p>\r\n<p><span class=\"MTConvertedEquation\">\\(BF = DE\\)</span> (cmt)</p>\r\n<p>Suy ra <span class=\"MTConvertedEquation\">\\(BFED\\)</span> là hình bình hành<strong></strong></p>","common_article":"","display_type":1,"vungoi_exam_id":"","article_type":1,"cmt_count":0,"zip_status":1,"last_modified_time":1699923673,"last_zip_time":1699923673,"zip_link":"https://offline.loigiaihay.com/articles/1391/141126/141126_1699923673.zip","picture":"https://img.loigiaihay.com/picture/article/2023/0612/1-0_6.png","youtube_id":"1hPyufKHLQA","video_start_time":"3833","quizlet_id":"0","ref_article_id":0,"readmore_display_type":0,"wiki":0,"comment_url":"https://loigiaihay.com/comment/giai-bai-4-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao-c1391a141126.html","origin_url":"https://loigiaihay.com/giai-bai-4-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao-c1391a141126.html","relate_link":[],"exam_file":"","solution_file":""},"callouts":[],"relate_articles":[],"others_in_cat":[{"article_id":141128,"cat_id":1391,"publish_time":1686537240,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_7.png","title":"Giải bài 5 trang 87 SGK Toán 8 tập 1– Chân trời sáng tạo","alias":"giai-bai-5-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao","introtext":"Lấy một tờ giấy, gấp làm tư để có một góc vuông ","display_type":1,"article_type":1},{"article_id":141125,"cat_id":1391,"publish_time":1686536940,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_4.png","title":"Giải bài 3 trang 87 SGK Toán 8 tập 1– Chân trời sáng tạo","alias":"giai-bai-3-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao","introtext":"Cho tam giác \r\n","display_type":1,"article_type":1},{"article_id":141124,"cat_id":1391,"publish_time":1686536820,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2023/0612/resize_1-0_3.png","title":"Giải bài 2 trang 87 SGK Toán 8 tập 1– Chân trời sáng tạo","alias":"giai-bai-2-trang-87-sgk-toan-8-tap-1-chan-troi-sang-tao","introtext":"Cho Hình 15. 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