Bài ôn tập chương 4: Tam giác bằng nhau

Home Lớp 7 Toán lớp 7 - Sách kết nối tri thức Bài ôn tập chương 4: Tam giác bằng nhauBài tập nâng cao

{"common":{"save":0,"post_id":"5679","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7581","post_id":"5679","mon_id":"1158532","chapter_id":"1158548","question":"Tính s\u1ed1 \u0111o c\u1ee7a góc ACD trong hình.<\/p><svg height=\"150\" width=\"240\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"242\" 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_16\"> <g id=\"svg_10\" transform=\"rotate(90 118.385009765625,74.90713500976564) \"> <g id=\"svg_4\"> <path d=\"m80.77,169.86664l0,-81.99999l84.00001,81.99999l-84.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/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=\"80\" x2=\"80\" y1=\"-29\" y2=\"89.14236\"><\/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=\"80\" x2=\"164\" y1=\"-27.85764\" y2=\"170.14236\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"72\" x2=\"86\" y1=\"40.14236\" y2=\"40.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"114\" x2=\"121\" y1=\"131.14236\" y2=\"119.14236\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"73\" xml:space=\"preserve\" y=\"140.14236\">=<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(90 117.00521850585936,171.80903625488284) \" x=\"110\" xml:space=\"preserve\" y=\"180.14236\">=<\/text> <rect fill=\"none\" fill-opacity=\"null\" height=\"10\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"10\" x=\"81\" y=\"160.14236\"><\/rect> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"15\" xml:space=\"preserve\" y=\"34.14236\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"101\" xml:space=\"preserve\" y=\"30.14236\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"11\" xml:space=\"preserve\" y=\"128.14236\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"215\" xml:space=\"preserve\" y=\"28.14236\">D<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A. <\/strong>22,5º","B. <\/strong>45º","C. <\/strong>67,5º","D. <\/strong>135º"],"correct":"3","level":"3","hint":"","answer":"Vì tam giác ABC vuông cân t\u1ea1i A  ($\\widehat{A}$<\/span> = 90º, AB = AC) nên $\\widehat{ABC}=\\widehat{ACB}$<\/span> = 45º<\/p>Ta có  $\\widehat{ABC}+\\widehat{DBC}=180^0$<\/span>  (hai góc k\u1ec1 bù)<\/p>⇒ $\\widehat{DBC}=180^0 - \\widehat{ABC}$<\/span> = 180º - 45º = 135º<\/p>Xét tam giác DBC cân t\u1ea1i B  (vì DB = BC)  có  $\\widehat{DBC }$<\/span> = 135º<\/p>⇒ $\\widehat{BDC}=\\widehat{BCD}$<\/span> = $(180^0 - \\widehat{DBC}) : 2$<\/span>  = (180º - 135º) : 2 = 22,5º<\/p>Ta có   $\\widehat{ACD}=\\widehat{ACB}+\\widehat{BCD}$<\/span> = 45º + 22,5º = 67,5º<\/p>\u0110áp án \u0111úng là   C. <\/strong>67,5º<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-04-29 15:07:01","option_type":"txt","len":1},{"id":"7582","post_id":"5679","mon_id":"1158532","chapter_id":"1158548","question":"Cho tam giác ABC \u0111\u1ec1u. L\u1ea5y các \u0111i\u1ec3m D , E , F theo th\u1ee9 t\u1ef1 thu\u1ed9c các c\u1ea1nh AB , BC , CA  sao cho AD = BE = CF. Tam giác DEF là tam giác gì?<\/p>","options":["A.<\/strong> Tam giác cân","B. <\/strong>Tam giác \u0111\u1ec1u","C. <\/strong>Tam giác vuông","D. <\/strong>Tam giác vuông cân"],"correct":"2","level":"3","hint":"","answer":"<svg height=\"180\" width=\"200\"> <g><title><\/title><rect fill=\"#fff\" height=\"182\" id=\"canvas_background\" width=\"202\" 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><text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"185\" xml:space=\"preserve\" y=\"161.14236\">C<\/text> <g id=\"svg_11\"> <g id=\"svg_3\" stroke=\"null\"> <path d=\"m25.74,149.3955l75.00001,-127.24073l75.00001,127.24073l-150.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path d=\"m141.63953,148.26128l-96.85158,-27.75315l74.64838,-66.5965l22.20321,94.34965z\" fill=\"#fff\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"93\" xml:space=\"preserve\" y=\"20.14236\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"13\" xml:space=\"preserve\" y=\"161.14236\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"28\" xml:space=\"preserve\" y=\"126.14236\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"139\" xml:space=\"preserve\" y=\"164.14236\">E<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"122\" xml:space=\"preserve\" y=\"52.14236\">F<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"60\" x2=\"78\" y1=\"61.14236\" y2=\"71.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"62\" x2=\"63\" y1=\"142.14236\" y2=\"157.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"143\" x2=\"155\" y1=\"108.14236\" y2=\"99.14236\"><\/line> <\/g> <\/svg><\/span><\/p>Ta có  AB = BC = CA   (tam giác ABC \u0111\u1ec1u)<\/p>          AD = BE = CF    (gi\u1ea3 thi\u1ebft)<\/p>Suy ra  AB - AD = BC - BE = CA - CF  hay  BD = CE = AF<\/p>Xét tam giác   ADF và tam giác BED có  AD = BE  (gi\u1ea3 thi\u1ebft) ,  $\\widehat{A}=\\widehat{B}$<\/span>  ( = 60º ) , AF = BD   (ch\u1ee9ng minh trên)<\/p>Suy ra  $\\triangle ADF =\\triangle BED $<\/span>  (c.g.c)  ⇒ DF = DE   (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng)   (1)<\/p>Xét tam giác   ADF và tam giác CFE có  AD = CF  (gi\u1ea3 thi\u1ebft) ,  $\\widehat{A}=\\widehat{C}$<\/span>  ( = 60º ) , AF = CE   (ch\u1ee9ng minh trên)<\/p>Suy ra  $\\triangle ADF =\\triangle CFE$<\/span>  (c.g.c)  ⇒ DF = EF   (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng)   (2)<\/p>T\u1eeb   (1)  và (2) ⇒ DF = DE = EF   ⇒  Tam giác DEF là tam giác \u0111\u1ec1u.<\/p>\u0110áp án \u0111úng là   B. <\/strong>Tam giác \u0111\u1ec1u<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-04-29 15:20:41","option_type":"txt","len":2},{"id":"7583","post_id":"5679","mon_id":"1158532","chapter_id":"1158548","question":"Cho hình v\u1ebd. Tính s\u1ed1 \u0111o  góc DAE.<\/p><svg height=\"140\" width=\"310\"> <g><title><\/title><rect fill=\"#fff\" height=\"142\" id=\"canvas_background\" width=\"312\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_2\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_20\"> <g id=\"svg_8\"> <g id=\"svg_5\"> <path d=\"m98.04,120.07477l53.00001,-91l53.00001,91l-106.00001,0l-0.00001,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path d=\"m169.64283,99.69095l0,-104.8749l107.19094,104.8749l-107.19094,0z\" fill=\"#fff\" id=\"svg_3\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(-30.414772033691406 223.23831176757812,47.253501892089865) \"><\/path> <path d=\"m26.07447,100.44331l0,-105.37961l106.32765,105.37961l-106.32765,0z\" fill=\"#fff\" id=\"svg_4\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(-59.687652587890625 79.23829650878905,47.753501892089844) \"><\/path> <\/g> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"10\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(-57.99463653564453 96.00000000000001,113.14236450195312) \" width=\"10\" x=\"91\" y=\"108.14236\"><\/rect> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"10\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(58 205.99998474121094,113.14234924316406) \" width=\"10\" x=\"201\" y=\"108.14236\"><\/rect> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"115\" x2=\"127\" y1=\"77.14236\" y2=\"82.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"172\" x2=\"186\" y1=\"82.14236\" y2=\"72.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"149\" x2=\"149\" y1=\"114.14236\" y2=\"128.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"48\" x2=\"52\" y1=\"96.14236\" y2=\"87.14236\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"247\" x2=\"255\" y1=\"90.14236\" y2=\"97.14236\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"147\" xml:space=\"preserve\" y=\"26.14236\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"83\" xml:space=\"preserve\" y=\"131.14236\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"205\" xml:space=\"preserve\" y=\"131.14236\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2\" xml:space=\"preserve\" y=\"63.14236\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"14\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"295\" xml:space=\"preserve\" y=\"60.14236\">E<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["90º","45º","120º","150º"],"correct":"4","level":"3","hint":"","answer":"Vì tam giác ABC có AB = AC = BC  (gi\u1ea3 thi\u1ebft) nên tam giác ABC là tam giác \u0111\u1ec1u<\/p>⇒ $\\widehat{BAC}=\\widehat{ABC}=\\widehat{ACB}$<\/span> = 60º <\/p>Vì  tam giác ABD vuông cân t\u1ea1i B   ( $\\widehat{ABD}$<\/span> = 90º , BA = BD )  nên  $\\widehat{BAD} = \\widehat{BDA}$<\/span> = 45º<\/p>Vì  tam giác ACE vuông cân t\u1ea1i C   ( $\\widehat{ACE}$<\/span> = 90º , CA = CE )  nên  $\\widehat{CAE} = \\widehat{CEA}$<\/span> = 45º<\/p>Ta có   $\\widehat{DAE}= \\widehat{DAB}+\\widehat{BAC}+\\widehat{CAE}$<\/span>   =  45º + 60º + 45º = 150º<\/p>\u0110áp án \u0111úng là   150º<\/strong><\/span><\/p>","type":"choose","extra_type":"flower","time":"0","user_id":"131","test":"1","date":"2022-04-29 15:35:03","option_type":"txt","len":0}]}