Hình thoi và hình vuông - Bài tập nâng cao

Home Lớp 8 Toán lớp 8 - Sách Kết nối tri thức Bài 14. Hình thoi và hình vuôngBài tập nâng cao

{"common":{"save":0,"post_id":"6573","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6127","post_id":"6573","mon_id":"1158921","chapter_id":"1158929","question":"Hình thoi MNPQ c\u1ea7n thêm \u0111i\u1ec1u ki\u1ec7n nào d\u01b0\u1edbi \u0111ây \u0111\u1ec3 nó là hình vuông?<\/p><svg height=\"150\" width=\"250\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"252\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_10\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_12\"> <g id=\"svg_6\"> <path d=\"m32.20477,75.89238l97.5,-43l97.5,43l-97.5,43l-97.5,-43z\" fill=\"#ffaad4\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.95453\" xml:space=\"preserve\" y=\"83.97727\">M<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"118.95453\" xml:space=\"preserve\" y=\"26.97727\">N<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"228.95453\" xml:space=\"preserve\" y=\"83.97727\">P<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"120.95453\" xml:space=\"preserve\" y=\"141.97726\">Q<\/text> <\/g> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"30.95453\" x2=\"225.95453\" y1=\"75.97727\" y2=\"76\"><\/line> <text fill=\"#000000\" 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(-14.524672508239746 81.45211791992195,62.84992599487302) matrix(0.8750202655792236,0,0,1,8.992857900870149,0) \" x=\"78.81151\" xml:space=\"preserve\" y=\"70.97726\">)<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(11.07744312286377 79.97705841064457,83.39272308349608) matrix(0.7155930207706974,0,0,0.8936115503311157,19.593864059234562,9.787924301168266) \" x=\"80.33918\" xml:space=\"preserve\" y=\"90.45348\">)<\/text> <line fill=\"none\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"129.95453\" x2=\"129.95453\" y1=\"31.97727\" y2=\"117.97726\"><\/line> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> MP &perp; NQ","B.<\/strong> MP = NQ","C.<\/strong> NM = PQ","D.<\/strong> $\\widehat{NMP}=\\widehat{QMP}$<\/span>"],"correct":"2","level":"3","hint":"Hình thoi có hai \u0111\u01b0\u1eddng chéo b\u1eb1ng nhau là hình vuông.<\/p>","answer":"Hình thoi MNPQ có hai \u0111\u01b0\u1eddng chéo MP = NQ thì nó là hình vuông.<\/p>Ch\u1ecdn B.<\/strong> MP = NQ<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 09:58:24","option_type":"math","len":0},{"id":"6128","post_id":"6573","mon_id":"1158921","chapter_id":"1158929","question":"Cho hình v\u1ebd, trong \u0111ó ABCD là hình vuông và các \u0111i\u1ec3m E, F, G, H l\u1ea7n l\u01b0\u1ee3t thu\u1ed9c các c\u1ea1nh AB, BC, CD, DA sao cho AE = BF = CG = DH. Nh\u1eadn xét nào sai<\/strong>?<\/p><svg height=\"240\" width=\"250\"> <g><title><\/title><rect fill=\"#fff\" height=\"242\" id=\"canvas_background\" width=\"252\" 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\"> <rect fill=\"#aaffd4\" height=\"183\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" width=\"182.99999\" x=\"23.95453\" y=\"30.97727\"><\/rect> <rect fill=\"#ffff56\" height=\"141\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(21.56201171875 115.45452880859366,122.47726440429688) \" width=\"141\" x=\"44.95453\" y=\"51.97727\"><\/rect> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"1.95453\" xml:space=\"preserve\" y=\"33.97727\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"210.95453\" xml:space=\"preserve\" y=\"32.97727\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"213.95453\" xml:space=\"preserve\" y=\"218.97726\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"1.95453\" xml:space=\"preserve\" y=\"224.97726\">D<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"66.95453\" xml:space=\"preserve\" y=\"22.97727\">E<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"213.95453\" xml:space=\"preserve\" y=\"88.97726\">F<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"145.95453\" xml:space=\"preserve\" y=\"235.97726\">G<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"0.95453\" xml:space=\"preserve\" y=\"170.97726\">H<\/text> <line fill=\"none\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"45.95453\" x2=\"42.95453\" y1=\"22.97727\" y2=\"38.97727\"><\/line> <line fill=\"none\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"197.95453\" x2=\"213.95453\" y1=\"50.97727\" y2=\"51.97727\"><\/line> <line fill=\"none\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"177.95453\" x2=\"177.95453\" y1=\"203.97726\" y2=\"218.97726\"><\/line> <line fill=\"none\" id=\"svg_15\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"12.95453\" x2=\"30.95453\" y1=\"189.97726\" y2=\"189.97726\"><\/line> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> EFGH là hình vuông.","B.<\/strong> EFGH có b\u1ed1n c\u1ea1nh b\u1eb1ng nhau.","C.<\/strong> EFGH có b\u1ed1n góc b\u1eb1ng nhau.","D.<\/strong> EFGH có b\u1ed1n góc nh\u1ecdn."],"correct":"4","level":"3","hint":"","answer":"Vì ABCD là hình vuông nên AB = BC = CD = AD.<\/p>Mà AE = BF = CG = DH nên EB = FC = GD = HA.<\/p>Suy ra b\u1ed1n tam giác AEH, BFE, CGF, DHG b\u1eb1ng nhau (theo tr\u01b0\u1eddng h\u1ee3p c.g.c).<\/p>Suy ra HE = EF = FG = GH. Do \u0111ó EFGH là hình thoi.<\/p>Ta có: $\\widehat{AEH}+\\widehat{HEF}+\\widehat{FEB}=180^0$<\/span><\/p>$\\widehat{AEH}+\\widehat{AHE}+\\widehat{HEF}=180^0$<\/span> (vì hai tam giác AEH và BFE b\u1eb1ng nhau nên $\\widehat{AHE}=\\widehat{FEB}$<\/span>)<\/p>$90^0+\\widehat{HEF}=180^0$<\/span> (vì tam giác AEH vuông \u1edf A nên $\\widehat{AEH}+\\widehat{AHE}=90^0$<\/span>)<\/p>Do \u0111ó $\\widehat{HEF}=90^0$<\/span>. Suy ra hình thoi EFGH là hình vuông.<\/p>A.<\/strong> EFGH là hình vuông. (\u0111úng)<\/p>B.<\/strong> EFGH có b\u1ed1n c\u1ea1nh b\u1eb1ng nhau. (\u0111úng)<\/p>C.<\/strong> EFGH có b\u1ed1n góc b\u1eb1ng nhau. (\u0111úng)<\/p>Ch\u1ecdn D.<\/strong> EFGH có b\u1ed1n góc nh\u1ecdn.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 10:09:36","option_type":"txt","len":2},{"id":"6129","post_id":"6573","mon_id":"1158921","chapter_id":"1158929","question":"Ch\u1ecdn câu \u0111úng v\u1ec1 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft hình vuông.<\/p>","options":["A.<\/strong> Hình ch\u1eef nh\u1eadt có hai góc k\u1ec1 b\u1eb1ng nhau là hình vuông.","B.<\/strong> Hình ch\u1eef nh\u1eadt có hai \u0111\u01b0\u1eddng chéo b\u1eb1ng nhau là hình vuông.","C.<\/strong> Hình ch\u1eef nh\u1eadt có m\u1ed9t \u0111\u01b0\u1eddng chéo là \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc là hình vuông.","D.<\/strong> Hình ch\u1eef nh\u1eadt có hai \u0111\u01b0\u1eddng chéo c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m m\u1ed7i \u0111\u01b0\u1eddng là hình vuông."],"correct":"3","level":"3","hint":"","answer":"Ch\u1ecdn C.<\/strong> Hình ch\u1eef nh\u1eadt có m\u1ed9t \u0111\u01b0\u1eddng chéo là \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t góc là hình vuông.<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"0","date":"2023-07-25 10:14:02","option_type":"txt","len":3}]}