{"segment":[{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho g\u00f3c vu\u00f4ng $\\widehat{xOy} $, \u0111i\u1ec3m A thu\u1ed9c tia Ox. <br\/> K\u1ebb tia Az vu\u00f4ng g\u00f3c v\u1edbi Ox (tia Az n\u1eb1m trong g\u00f3c $\\widehat{xOy} $). <br\/> G\u1ecdi Om l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xOy} $, An l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xAz} $ <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh Om \/\/ An ","temp":"sequence","correct":[[[1],[5],[2],[3],[4],[6]]],"list":[{"point":10,"image":"","left":["Ta c\u00f3 Om l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xOy} $ "," Do d\u00f3 $\\widehat{mOx} = \\widehat{nAx} (= 45^{o}) $"," n\u00ean $\\widehat{mOx} = 45^{o} $ "," M\u1eb7t kh\u00e1c An l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xAz} $ ","n\u00ean $\\widehat{nAx} = 45^{o} $ ","V\u1eady Om \/\/ An "],"top":55,"hint":"","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-59.png' \/><\/center> <br\/>Ta c\u00f3 Om l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xOy} $ <br\/> n\u00ean $\\widehat{mOx} = \\dfrac{\\widehat{xOy}}{2} = \\dfrac{90^{o}}{2} = 45^{o} $ <br\/> M\u1eb7t kh\u00e1c An l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xAz} $ <br\/> n\u00ean $\\widehat{nAx} = \\dfrac{\\widehat{xAz}}{2} = \\dfrac{90^{o}}{2} = 45^{o} $ <br\/> Do d\u00f3 $\\widehat{mOx} = \\widehat{nAx} (= 45^{o}) $ <br\/> Hai g\u00f3c n\u00e0y l\u00e0 hai g\u00f3c \u0111\u1ed3ng v\u1ecb t\u1ea1o b\u1edfi Ox c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng Om v\u00e0 An n\u00ean Om \/\/ An. <br\/> V\u1eady Om \/\/ An "}]}],"id_ques":1441},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd, bi\u1ebft $\\widehat{A_{1}} = 72^{o}; \\widehat{B_{2}} = \\dfrac{2}{3}\\widehat{B_{1}} $ <br\/> H\u00e3y s\u1eafp x\u1ebfp ch\u1ee9ng minh a \/\/ b. ","temp":"sequence","correct":[[[2],[3],[5],[1],[4]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-19.png","left":["m\u00e0 $\\widehat{B_{2}} = \\dfrac{2}{3}\\widehat{B_{1}} $","n\u00ean $\\widehat{B_{2}} = 72^{o} $","V\u1eady a \/\/ b (v\u00ec c\u00f3 c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau)","Ta c\u00f3: $\\widehat{B_{1}} + \\widehat{B_{2}} = 180^{o} $(k\u1ec1 b\u00f9) ","Suy ra: $\\widehat{A_{1}} = \\widehat{B_{2}} (= 72^{o}) $, l\u1ea1i c\u00f3 $\\widehat{A_{1}}$ v\u00e0 $\\widehat{B_{2}}$ \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb v\u1edbi nhau"],"top":70,"hint":"","explain":"Ta c\u00f3: $\\widehat{B_{1}} + \\widehat{B_{2}} = 180^{o} $(k\u1ec1 b\u00f9), m\u00e0 $\\widehat{B_{2}} = \\dfrac{2}{3}\\widehat{B_{1}} $ <br\/> n\u00ean: $\\dfrac{\\widehat{B_{2}}}{2} = \\dfrac{\\widehat{B_{1}}}{3} = \\dfrac{\\widehat{B_{2}}+\\widehat{B_{1}}}{2+3} = \\dfrac{180^{o}}{5} = 36^{o} \\\\ \\Rightarrow\\widehat{B_{2}} = 36^{o}.2 = 72^{o} $ <br\/> Suy ra: $\\widehat{A_{1}} = \\widehat{B_{2}} (= 72^{o}) $<br\/>L\u1ea1i c\u00f3: $\\widehat{A_{1}}$ v\u00e0 $\\widehat{B_{2}}$ \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb v\u1edbi nhau <br\/> V\u1eady a \/\/ b (v\u00ec c\u00f3 c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau) "}]}],"id_ques":1442},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh By \/\/ Cz","temp":"sequence","correct":[[[1],[4],[5],[3],[2],[6]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-55A.png","left":["Trong g\u00f3c aBC v\u1ebd tia By' l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia By","n\u00ean $\\widehat{y'BC} = 40^{o} $","Do \u0111\u00f3 $\\widehat{y'BC} = \\widehat{BCz} $ ","Bi\u1ebft By' n\u1eb1m gi\u1eefa hai tia Ba v\u00e0 BC","n\u00ean $\\widehat{aBy'} = 70^{o} $ ","V\u1eady By \/\/ Cz"],"top":55,"hint":"","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-55B.png' \/><\/center> <br\/> Trong g\u00f3c aBC v\u1ebd tia By' l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia By <br\/> n\u00ean $\\widehat{aBy'} = 180^{o} - 110^{o} = 70^{o} $ <br\/> Bi\u1ebft By' n\u1eb1m gi\u1eefa hai tia Ba v\u00e0 BC <br\/> $\\Rightarrow \\widehat{aBy'} + \\widehat{y'BC} = \\widehat{aBC} \\\\ \\Rightarrow \\widehat{y'BC} = 110^{o} - 70^{o} = 40^{o} $ <br\/> Do \u0111\u00f3 $\\widehat{y'BC} = \\widehat{BCz} (= 40^{o}) $ <br\/> Hai g\u00f3c n\u00e0y l\u00e0 hai g\u00f3c so le trong t\u1ea1o b\u1edfi BC c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng yy' v\u00e0 Cz n\u00ean yy' \/\/ Cz. <br\/> V\u1eady By \/\/ Cz "}]}],"id_ques":1443},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","ques":" Cho h\u00ecnh v\u1ebd ","correct":[["t","f","t","f","t"]],"list":[{"point":10,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["Hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.","Hai \u0111\u01b0\u1eddng th\u1eb3ng song song th\u00ec kh\u00f4ng c\u1eaft nhau.","Hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft nhau, kh\u00f4ng tr\u00f9ng nhau.","Hai \u0111o\u1ea1n th\u1eb3ng song song l\u00e0 hai \u0111o\u1ea1n th\u1eb3ng kh\u00f4ng c\u1eaft nhau.","Hai \u0111o\u1ea1n th\u1eb3ng song song l\u00e0 hai \u0111o\u1ea1n th\u1eb3ng n\u1eb1m tr\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t kh\u00f4ng c\u1eaft nhau."],"hint":"","explain":["\u0110\u00fang","<br\/> Sai. V\u00ec ch\u00fang c\u00f3 th\u1ec3 tr\u00f9ng nhau","<br\/> \u0110\u00fang","<br\/> Sai. V\u00ed d\u1ee5: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-41A.png' \/><\/center> ","<br\/> \u0110\u00fang"]}]}],"id_ques":1444},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","ques":" Cho h\u00ecnh v\u1ebd ","correct":[["t","t","f","f","t","t"]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-54.png","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["$\\widehat{A_{4}} = \\widehat{B_{2}} = 135^{o} $ ","$\\widehat{A_{1}} = \\widehat{B_{1}} = 45^{o} $","$\\widehat{A_{2}} = \\widehat{B_{3}} = 135^{o} $","$\\widehat{A_{4}} = 135^{o}, \\widehat{B_{2}} = 45^{o} $","$\\widehat{A_{1}} = \\widehat{B_{3}} = 45^{o} $","$\\widehat{A_{2}} = \\widehat{B_{4}} = 135^{o} $"],"hint":"","explain":["\u0110\u00fang. $\\widehat{A_{4}} = \\widehat{B_{2}} = 180^{o} - 45^{o} = 135^{o} $ (c\u1eb7p g\u00f3c so le trong) ","<br\/> \u0110\u00fang. $\\widehat{A_{1}} = \\widehat{B_{1}} = 45^{o} $ (c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb)"," <br\/> Sai. V\u00ec : $\\widehat{B_{3}} = 45^{o} $"," <br\/> Sai. V\u00ec : $\\widehat{B_{2}} = 135^{o} $","<br\/> \u0110\u00fang (c\u1eb7p g\u00f3c so le ngo\u00e0i)","<br\/> \u0110\u00fang (c\u1eb7p g\u00f3c so le ngo\u00e0i)"]}]}],"id_ques":1445},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho $\\widehat{xOy} = 150^{o} $. Tr\u00ean tia Ox l\u1ea5y \u0111i\u1ec3m A r\u1ed3i k\u1ebb tia Az n\u1eb1m trong g\u00f3c xOy sao cho $\\widehat{OAz} = 30^{o} $. K\u1ebb tia Az' l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Az. <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh zz' \/\/ Oy. ","temp":"sequence","correct":[[[1],[4],[3],[2],[5]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-52A.png","left":["K\u1ebb tia Oy' l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oy","Do \u0111\u00f3 $\\widehat{AOy'} = \\widehat{OAz} $","n\u00ean $\\widehat{AOy'} = 30^{o} $","th\u00ec $\\widehat{y'OA} + \\widehat{AOy} = 180^{o} $","V\u1eady zz' \/\/ Oy"],"top":55,"hint":"","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-52B.png' \/><\/center> <br\/> K\u1ebb tia Oy' l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oy th\u00ec $\\widehat{AOy'} + \\widehat{AOy} = 180^{o} $(hai g\u00f3c k\u1ec1 b\u00f9) <br\/> $\\Rightarrow \\widehat{AOy'} = 180^{o} - \\widehat{AOy} = 180^{o} - 150^{o} = 30^{o} $ Do \u0111\u00f3 $\\widehat{AOy'} = \\widehat{OAz} (= 30^{o} ) $<br\/>L\u1ea1i c\u00f3: $\\widehat{AOy'}$ v\u00e0 $\\widehat{OAz}$ \u1edf v\u1ecb tr\u00ed so le trong v\u1edbi nhau <br\/> V\u1eady z'z \/\/ y'y (v\u00ec c\u00f3 c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau) hay z'z \/\/ Oy "}]}],"id_ques":1446},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd, bi\u1ebft r\u1eb1ng tia Cx l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{ACy} $ <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh Cx \/\/ AB. ","temp":"sequence","correct":[[[3],[2],[5],[1],[4],[6]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C15-14.png","left":["M\u1eb7t kh\u00e1c Cx l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{ACy} $ ","n\u00ean $\\widehat{ACy} = 130^{o} $","Do \u0111\u00f3 $\\widehat{xCy} = \\widehat{ABC} $","Ta c\u00f3 $\\widehat{ACB} + \\widehat{ACy} = 180^{o} $","n\u00ean $\\widehat{xCy} = 65^{o} $","V\u1eady Cx \/\/ AB "],"top":70,"hint":"","explain":"Ta c\u00f3 $\\widehat{ACB} + \\widehat{ACy} = 180^{o} $(hai g\u00f3c k\u1ec1 b\u00f9) <br\/> n\u00ean $\\widehat{ACy} = 180^{o} - \\widehat{ACB} = 180^{o} - 50^{o} = 130^{o} $ <br\/> M\u1eb7t kh\u00e1c Cx l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{ACy} $ n\u00ean <br\/> $\\widehat{xCy} = \\dfrac{\\widehat{ACy}}{2} = \\dfrac{130^{o}}{2} = 65^{o} $ <br\/> Do \u0111\u00f3 $\\widehat{xCy} = \\widehat{ABC} (= 65^{o})$ <br\/>V\u1eady Cx \/\/ AB (v\u00ec c\u00f3 c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau). "}]}],"id_ques":1447},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","ques":"","correct":[["t","t","t","f"]],"list":[{"point":10,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["Hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft nhau","Hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung","Hai \u0111\u01b0\u1eddng th\u1eb3ng a, b song song v\u1edbi nhau \u0111\u01b0\u1ee3c k\u00ed hi\u1ec7u l\u00e0 a \/\/ b","N\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng c c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng a, b v\u00e0 trong c\u00e1c g\u00f3c t\u1ea1o th\u00e0nh c\u00f3 m\u1ed9t c\u1eb7p g\u00f3c trong c\u00f9ng ph\u00eda b\u1eb1ng nhau th\u00ec a v\u00e0 b song song v\u1edbi nhau. "],"hint":"","explain":["Sai. V\u00ec ch\u00fang c\u00f3 th\u1ec3 tr\u00f9ng nhau. ","<br\/> \u0110\u00fang","<br\/> \u0110\u00fang","<br\/> Sai. V\u00ec: Hai g\u00f3c trong c\u00f9ng ph\u00eda b\u00f9 nhau th\u00ec a \/\/ b "]}]}],"id_ques":1448},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd, bi\u1ebft $\\widehat{A_{1}} = 60^{o}; \\widehat{B_{1}} = \\dfrac{1}{2}\\widehat{B_{2}} $ <br\/> H\u00e3y s\u1eafp x\u1ebfp ch\u1ee9ng minh a \/\/ b. ","temp":"sequence","correct":[[[2],[3],[5],[1],[4]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-17.png","left":["m\u00e0 $\\widehat{B_{1}} = \\dfrac{1}{2}\\widehat{B_{2}} $","n\u00ean $\\widehat{B_{1}} = 60^{o} $","V\u1eady a \/\/ b (v\u00ec c\u00f3 c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau)","Ta c\u00f3: $\\widehat{B_{1}} + \\widehat{B_{2}} = 180^{o} $(k\u1ec1 b\u00f9) ","Suy ra: $\\widehat{A_{1}} = \\widehat{B_{1}} (= 60^{o}) $"],"top":70,"hint":"","explain":"Ta c\u00f3: $\\widehat{B_{1}} + \\widehat{B_{2}} = 180^{o} $(k\u1ec1 b\u00f9), m\u00e0 $\\widehat{B_{1}} = \\dfrac{1}{2}\\widehat{B_{2}} $ <br\/> n\u00ean $\\dfrac{\\widehat{B_{1}}}{1} = \\dfrac{\\widehat{B_{2}}}{2} = \\dfrac{\\widehat{B_{1}}+\\widehat{B_{2}}}{1+2} = \\dfrac{180^{o}}{3} = 60^{o} \\\\ \\Rightarrow\\widehat{B_{1}} = 60^{o} $ <br\/> Suy ra: $\\widehat{A_{1}} = \\widehat{B_{1}} (= 60^{o}) $ <br\/> V\u1eady a \/\/ b (v\u00ec c\u00f3 c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau) <\/span>"}]}],"id_ques":1449},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd, bi\u1ebft $\\widehat{APM} + \\widehat{MPB} + \\widehat{PQD} = 216^{o} $ v\u00e0 $\\widehat{APM} = 4\\widehat{MPB}$ <br\/> H\u00e3y s\u1eafp x\u1ebfp ch\u1ee9ng minh AB \/\/ CD ","temp":"sequence","correct":[[[3],[4],[2],[5],[1]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai4/lv3/img\/H7C14-11.png","left":["M\u1eb7t kh\u00e1c, do $\\widehat{APM} + \\widehat{MPB} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> v\u00e0 $\\widehat{APM} = 4\\widehat{MPB}$ (gi\u1ea3 thi\u1ebft)","n\u00ean $ 6\\widehat{MPB} = 180^{o} \\Rightarrow \\widehat{MPB} = 36^{o} $","do \u0111\u00f3 $\\widehat{PQD} = 216^{o} - 180^{o} = 36^{o} $","Hai g\u00f3c $\\widehat{MPB}$ v\u00e0 $\\widehat{PQD}$ \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb v\u00e0 $\\widehat{MPB} = \\widehat{PQD} = 36^{o} $. <br\/> V\u1eady AB \/\/ CD ","Ta c\u00f3: $\\widehat{APM} + \\widehat{MPB} + \\widehat{PQD} = 216^{o} $ (gi\u1ea3 thi\u1ebft), <br\/> m\u00e0 $\\widehat{APM} + \\widehat{MPB} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9) "],"top":100,"hint":"","explain":"<span class='basic_left'>Ta c\u00f3: $\\widehat{APM} + \\widehat{MPB} + \\widehat{PQD} = 216^{o} $ (gi\u1ea3 thi\u1ebft), <br\/> M\u00e0 $\\widehat{APM} + \\widehat{MPB} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9)<br\/>Do \u0111\u00f3 $\\widehat{PQD} = 216^{o} - 180^{o} = 36^{o} $ (1)<br\/>M\u1eb7t kh\u00e1c $\\widehat{APM} + \\widehat{MPB} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9), $\\widehat{APM} = 4\\widehat{MPB}$ (gi\u1ea3 thi\u1ebft)<br\/>N\u00ean $ 6\\widehat{MPB} = 180^{o} \\Rightarrow \\widehat{MPB} = 36^{o} $ (2)<br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{MPB} = \\widehat{PQD}$<br\/>L\u1ea1i c\u00f3: Hai g\u00f3c $\\widehat{MPB}$ v\u00e0 $\\widehat{PQD}$ \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb<br\/>V\u1eady AB \/\/ CD<\/span>"}]}],"id_ques":1450}],"lesson":{"save":0,"level":3}}