Hình chữ nhật - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài 13. Hình chữ nhậtBài tập nâng cao

{"common":{"save":0,"post_id":"6570","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6105","post_id":"6570","mon_id":"1158921","chapter_id":"1158929","question":"Cho tam giác ABC vuông t\u1ea1i A có M, N, P  l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a BC, CA, AB. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là \u0111úng<\/strong>?<\/p>","options":["A.<\/strong> MA = MB = MC = $\\dfrac{BC}{2}$<\/span>","B.<\/strong> NB = NC = NA = $\\dfrac{AC}{2}$<\/span>","C.<\/strong> PC = PB = PA = $\\dfrac{AB}{2}$<\/span>","D<\/strong>. MA = MB = MC = $\\dfrac{AB}{2}$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<svg height=\"190\" width=\"160\"> <g><title><\/title><rect fill=\"#fff\" height=\"192\" id=\"canvas_background\" width=\"162\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_16\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_15\"> <path d=\"m22.07877,167.41512l0,-149.00001l118.00001,149.00001l-118.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.31535\" xml:space=\"preserve\" y=\"97.52273\">P<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_3\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"78.31535\" xml:space=\"preserve\" y=\"185.52273\">N<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_4\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"93.31535\" xml:space=\"preserve\" y=\"94.52273\">M<\/text> <rect fill=\"#fff\" height=\"12\" id=\"svg_6\" stroke=\"#000\" stroke-width=\"1.5\" width=\"12\" x=\"22.31535\" y=\"154.52273\"><\/rect> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"21.31535\" x2=\"83.31535\" y1=\"166.52273\" y2=\"97.52273\"><\/line> <ellipse cx=\"83.81535\" cy=\"97.02273\" fill=\"#ff0000\" id=\"svg_7\" rx=\"2.5\" ry=\"2.5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"84\" cy=\"167.02273\" fill=\"#ff0000\" id=\"svg_8\" rx=\"2.5\" ry=\"2.5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"21.81535\" cy=\"97.02273\" fill=\"#ff0000\" id=\"svg_9\" rx=\"2.5\" ry=\"2.5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"49.31535\" x2=\"60.31535\" y1=\"62.52273\" y2=\"54.52273\"><\/line> <line fill=\"none\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"106.31535\" x2=\"115.31535\" y1=\"134.52273\" y2=\"126.52273\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"8.31535\" xml:space=\"preserve\" y=\"172.52273\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"7.31535\" xml:space=\"preserve\" y=\"17.52273\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"143.31535\" xml:space=\"preserve\" y=\"178.52273\">C<\/text> <\/g> <line fill=\"none\" id=\"svg_17\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"49.31535\" x2=\"61.31535\" y1=\"118.52273\" y2=\"131.52273\"><\/line> <\/g> <\/svg><\/span><\/p>Vì M là trung \u0111i\u1ec3m c\u1ee7a BC nên MB = MC = $\\dfrac{BC}{2}$<\/span> .<\/p>Vì tam giác ABC vuông t\u1ea1i A có M là trung \u0111i\u1ec3m c\u1ee7a BC nên AM là \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n BC.<\/p>⇒ AM = $\\dfrac{BC}{2}$<\/span> .<\/p>T\u1eeb \u0111ó suy ra  MA = MB = MC = $\\dfrac{BC}{2}$<\/span> .<\/p>\u0110áp án \u0111úng là   A.<\/strong> MA = MB = MC = $\\dfrac{BC}{2}$<\/span> .<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 08:39:22","option_type":"math","len":0},{"id":"6107","post_id":"6570","mon_id":"1158921","chapter_id":"1158929","question":"Câu nào sau \u0111ây là \u0111úng<\/strong>?<\/p>","options":["A.<\/strong> T\u1ee9 giác có t\u1ea5t c\u1ea3 các góc b\u1eb1ng nhau là hình ch\u1eef nh\u1eadt.","B.<\/strong> T\u1ee9 giác có t\u1ea5t c\u1ea3 các c\u1ea1nh b\u1eb1ng nhau là hình ch\u1eef nh\u1eadt.","C.<\/strong> T\u1ee9 giác có hai c\u1ea1nh \u0111\u1ed1i v\u1eeba song song v\u1eeba b\u1eb1ng nhau là hình ch\u1eef nh\u1eadt.","D.<\/strong> T\u1ee9 giác có hai \u0111\u01b0\u1eddng chéo b\u1eb1ng nhau là hình ch\u1eef nh\u1eadt."],"correct":"1","level":"3","hint":"","answer":"Câu \u0111úng là   A.<\/strong> T\u1ee9 giác có t\u1ea5t c\u1ea3 các góc b\u1eb1ng nhau là hình ch\u1eef nh\u1eadt.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 08:43:00","option_type":"txt","len":3},{"id":"6111","post_id":"6570","mon_id":"1158921","chapter_id":"1158929","question":"Cho tam giác ABC là tam giác vuông t\u1ea1i A. K\u1ebb \u0111\u01b0\u1eddng cao AH (H ∈ BC). Qua A k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi BC và qua C k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi AH. Hai \u0111\u01b0\u1eddng th\u1eb3ng này c\u1eaft nhau t\u1ea1i K. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là \u0111úng nh\u1ea5t<\/strong>?<\/p>","options":["A.<\/strong> AHCK là hình bình hành.","B.<\/strong> AHCK là hình ch\u1eef nh\u1eadt.","C.<\/strong> C\u1ea3 A và B \u0111\u1ec1u sai.","D.<\/strong> C\u1ea3 A và B \u0111\u1ec1u \u0111úng."],"correct":"4","level":"3","hint":"","answer":"<svg height=\"120\" width=\"205\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"122\" id=\"canvas_background\" width=\"207\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_12\"> <g id=\"svg_5\"> <path d=\"m54.10377,166.42512l0,-139l92,139l-92,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(124 100.10377502441406,96.9251174926758) \"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"68.31535\" x2=\"68.31535\" y1=\"20.52273\" y2=\"97.52273\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"68.31535\" x2=\"183\" y1=\"19.52273\" y2=\"20\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"183.31535\" x2=\"183.31535\" y1=\"96.52273\" y2=\"20\"><\/line> <\/g> <rect fill=\"none\" fill-opacity=\"null\" height=\"11\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"11\" x=\"68.31535\" y=\"85.52273\"><\/rect> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"59.31535\" xml:space=\"preserve\" y=\"15.52273\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.31535\" xml:space=\"preserve\" y=\"105.52273\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"185.31535\" xml:space=\"preserve\" y=\"108.52273\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"63.31535\" xml:space=\"preserve\" y=\"113.52273\">H<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"186.31535\" xml:space=\"preserve\" y=\"19.52273\">K<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Xét t\u1ee9 giác AHCK có AH \/\/ CK  (cách v\u1ebd) và AK \/\/ HC  (cách v\u1ebd).<\/p>Suy ra t\u1ee9 giác AHCK là hình bình hành. (1)  (suy ra A \u0111úng)<\/p>(T\u1ee9 giác có các c\u1ea1nh \u0111\u1ed1i song song là hình bình hành).<\/p>M\u1eb7t khác $\\widehat{AHC}$<\/span> = 90°  (AH là \u0111\u01b0\u1eddng cao).  (2)<\/p>T\u1eeb (1) và (2) suy ra hình bình hành AHCK là hình ch\u1eef nh\u1eadt.  (suy ra B \u0111úng).<\/p>(Hình bình hành có m\u1ed9t góc vuông là hình ch\u1eef nh\u1eadt).<\/p>Do \u0111ó \u0111áp án \u0111úng nh\u1ea5t là   D.<\/strong> C\u1ea3 A và B \u0111\u1ec1u \u0111úng.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 08:55:41","option_type":"txt","len":3}]}