{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> N\u1ebfu h\u00ecnh thang c\u00f3 hai c\u1ea1nh b\u00ean song song th\u00ec: <\/span>","select":["A. Hai c\u1ea1nh b\u00ean b\u1eb1ng nhau ","B. Hai c\u1ea1nh \u0111\u00e1y b\u1eb1ng nhau ","C. Hai c\u1ea1nh b\u00ean b\u1eb1ng nhau v\u00e0 hai c\u1ea1nh \u0111\u00e1y b\u1eb1ng nhau "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_1.jpg' \/><\/center> <span class='basic_left'> N\u1ed1i $A$ v\u1edbi $C$. <br\/> X\u00e9t h\u00ecnh thang $ABCD$$(AB\/\/CD)$ c\u00f3 $AD\/\/BC$<br\/>X\u00e9t hai tam gi\u00e1c $ABC$ v\u00e0 $CDA$ c\u00f3: <br\/> + $\\widehat{A_1}=\\widehat{C_1}$ (do $AB \/\/ DC$) <br\/> + $AC$ c\u1ea1nh chung <br\/> + $\\widehat {A_2}=\\widehat{C_2}$ (do $AD \/\/ BC$) <br\/> $\\Rightarrow \\Delta ABC = \\Delta CDA $ (g - c - g) <br\/> $\\Rightarrow AB = DC; AD=BC$ (c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><\/span> ","column":1}]}],"id_ques":1311},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" <span class='basic_left'> H\u00ecnh thang vu\u00f4ng l\u00e0: <\/span>","select":["A. T\u1ee9 gi\u00e1c c\u00f3 hai g\u00f3c vu\u00f4ng ","B. T\u1ee9 gi\u00e1c c\u00f3 hai g\u00f3c k\u1ec1 v\u1edbi m\u1ed9t c\u1ea1nh b\u1eb1ng nhau ","C. H\u00ecnh thang c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_2.jpg' \/><\/center> <span class='basic_left'>Theo \u0111\u1ecbnh ngh\u0129a: H\u00ecnh thang vu\u00f4ng l\u00e0 h\u00ecnh thang c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng. <br\/> Do \u0111\u00f3, \u0111\u00e1p \u00e1n C l\u00e0 \u0111\u00fang. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><\/span> ","column":1}]}],"id_ques":1312},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> T\u00ednh hi\u1ec7u s\u1ed1 \u0111o hai g\u00f3c c\u00f9ng k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean. Bi\u1ebft s\u1ed1 \u0111o m\u1ed9t trong hai g\u00f3c \u0111\u00f3 l\u00e0 $60^{o}$ <\/span>","select":["A. $40^o$ ","B. $60^o$ ","C. $120^o$ ","D. $140^o$ "],"hint":" Trong h\u00ecnh thang: T\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean l\u00e0 $180^o$.","explain":" <span class='basic_left'> Trong h\u00ecnh thang: Hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u00f3 t\u1ed5ng s\u1ed1 \u0111o l\u00e0 $180^o$. <br\/> M\u00e0 m\u1ed9t g\u00f3c c\u00f3 s\u1ed1 \u0111o l\u00e0 $60^o$ n\u00ean g\u00f3c c\u00f2n l\u1ea1i l\u00e0 $120^o$ <br\/> Hi\u1ec7u gi\u1eefa hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean l\u00e0: $120^o-60^o=60^o$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":1313},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["="],["="],["="]]],"list":[{"point":5,"width":40,"type_input":"","ques":"<span class='basic_left'> H\u00ecnh thang c\u00e2n $ABCD\\, (AB \/\/ CD; AB < CD)$; $O=AC\\cap BD$. <br\/> So s\u00e1nh: <br\/> $AC \\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\,BD$ <br\/> $OD\\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\, OC $ <br\/> $OA \\, \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\, OB$ ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_3.jpg' \/><\/center> <span class='basic_left'> Do $ABCD\\, (AB \/\/ CD)$ l\u00e0 h\u00ecnh thang c\u00e2n n\u00ean $AC = BD$. <br\/> Ta d\u1ec5 d\u00e0ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c $\\Delta ACD = \\Delta BDC$ (c - c - c) <br\/> $\\Rightarrow \\widehat {A_1}=\\widehat {B_1}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> T\u01b0\u01a1ng t\u1ef1, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c: $\\widehat {D_1}= \\widehat {C_1}$ <br\/> X\u00e9t hai tam gi\u00e1c $AOD$ v\u00e0 $BOC$ c\u00f3: <br\/> + $\\widehat {A_1}=\\widehat {B_1}$ (ch\u1ee9ng minh tr\u00ean) <br\/> + $AD = BC$ (gi\u1ea3 thi\u1ebft) <br\/> + $\\widehat {D_1}=\\widehat {C_1}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow \\Delta AOD = \\Delta BOC$ (g - c - g) <br\/> Do \u0111\u00f3 $AO = OB; DO = CO$ (c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng). <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng d\u1ea5u '='. <\/span><\/span> "}]}],"id_ques":1314},{"time":14,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["135"]]],"list":[{"point":10,"width":40,"type_input":"","ques":" <span class='basic_left'> T\u1ee9 gi\u00e1c $ABCD$ bi\u1ebft $\\widehat{A}=\\widehat{B}={{90}^{o}};\\,\\,AB=BC=\\dfrac{1}{2}AD$. <br\/> <br\/> <b> C\u00e2u 1:<\/b> T\u00ednh $\\widehat {BCD}$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n :<\/b> <br\/> $\\widehat{BCD}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span> ","hint":"K\u1ebb $CE\\bot AD$ <br\/> Ch\u1ee9ng minh $CED$ vu\u00f4ng c\u00e2n.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_4.jpg' \/><\/center> K\u1ebb $CE\\bot AD$ <br\/> Ta c\u00f3 $AB\\bot AD\\,(\\text{gi\u1ea3 thi\u1ebft})\\Rightarrow CE\/\/AB$ (t\u1eeb vu\u00f4ng g\u00f3c t\u1edbi song song)<br\/> M\u00e0 $\\left. \\begin{align} & AB\\bot BC\\,(\\text{gi\u1ea3 thi\u1ebft}) \\\\ & AD\\bot AB\\,\\left( \\text{gi\u1ea3 thi\u1ebft} \\right) \\\\ \\end{align} \\right\\}\\Rightarrow BC\/\/AD$ (t\u1eeb vu\u00f4ng g\u00f3c t\u1edbi song song) <br\/> Suy ra $CE= AB, BC= AE$ (t\u00ednh ch\u1ea5t \u0111o\u1ea1n ch\u1eafn)<br\/> M\u00e0 $AB=BC=\\dfrac{1}{2}AD$ $\\Rightarrow CE=AE=ED$<br\/> X\u00e9t $\\Delta CED$ c\u00f3 $\\widehat{CED}={{90}^{o}}$ ; $CE = ED$ (ch\u1ee9ng minh tr\u00ean) <br\/>$ \\Rightarrow \\Delta CED$ vu\u00f4ng c\u00e2n (\u0111\u1ecbnh l\u00ed)<br\/> $\\Rightarrow \\widehat{ECA}=\\widehat{D}=\\dfrac{{{90}^{o}}}{2}={{45}^{o}}$<br\/> M\u00e0 $ABCE$ l\u00e0 h\u00ecnh vu\u00f4ng v\u00ec c\u00f3 ba g\u00f3c vu\u00f4ng v\u00e0 b\u1ed1n c\u1ea1nh b\u1eb1ng nhau $\\Rightarrow \\widehat{BCE}={{90}^{o}}$ <br\/>$\\Rightarrow \\widehat{BCD}={{90}^{o}}+{{45}^{o}}={{135}^{o}}$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $\\widehat{BCD}=135^o$. <\/span><\/span> "}]}],"id_ques":1315},{"time":14,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["90"]]],"list":[{"point":10,"width":40,"type_input":"","ques":" <span class='basic_left'> T\u1ee9 gi\u00e1c $ABCD$ bi\u1ebft $\\widehat{A}=\\widehat{B}={{90}^{o}};\\,\\,AB=BC=\\dfrac{1}{2}AD$. <br\/> <br\/> <b> C\u00e2u 2:<\/b> T\u00ednh $\\widehat{ACD}$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $\\widehat{ACD}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^o$ <\/span>","hint":" X\u00e9t d\u1ea1ng c\u1ee7a tam gi\u00e1c $ACD$.","explain":"<span class='basic_left'> V\u1ebd h\u00ecnh <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_4.jpg' \/><\/center> <b>C\u00e1ch 1:<\/b> X\u00e9t $\\Delta ACD $ c\u00f3:<br\/> $CE\\bot AD\\,\\,(\\text{gi\u1ea3 thi\u1ebft});\\,AE=ED\\,\\,(\\text{ch\u1ee9ng minh tr\u00ean})$ <br\/> $\\Rightarrow \\Delta$ $ACD$ c\u00e2n (t\u00ednh ch\u1ea5t)<br\/> $\\Rightarrow \\widehat{CAD}=\\widehat{ACE}={{45}^{o}}\\,(\\text{t\u00ednh ch\u1ea5t})\\Rightarrow \\widehat{ACD}={{90}^{o}} $ <br\/><b>C\u00e1ch 2:<\/b> Tam gi\u00e1c $ACD$ c\u00f3 $CE = AB=\\dfrac{AD}{2}$(ch\u1ee9ng minh c\u00e2u 1) <br\/>N\u00ean tam gi\u00e1c $ACD$ vu\u00f4ng t\u1ea1i $C$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn b\u1eb1ng n\u1eeda c\u1ea1nh \u0111\u1ed1i)<br\/>V\u1eady $\\widehat{ACD}=90^{o}$<br\/> <span class='basic_pink'> Do \u0111\u00f3 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $90$. <\/span><\/span> "}]}],"id_ques":1316},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","temp":"true_false","correct":[["t","t","f"]],"list":[{"point":5,"col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":["H\u00ecnh thang l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 hai c\u1ea1nh \u0111\u1ed1i song song "," M\u1ecdi t\u00ednh ch\u1ea5t c\u00f3 \u1edf t\u1ee9 gi\u00e1c th\u00ec c\u0169ng c\u00f3 \u1edf h\u00ecnh thang"," M\u1ecdi t\u00ednh ch\u1ea5t c\u00f3 \u1edf h\u00ecnh thang th\u00ec c\u0169ng c\u00f3 \u1edf t\u1ee9 gi\u00e1c"],"explain":[" <span class='basic_left'><b> 1 - \u0110\u00fang<\/b>: Theo \u0111\u1ecbnh ngh\u0129a \u0111\u00e3 h\u1ecdc v\u1ec1 h\u00ecnh thang <br\/> <\/span> ","<span class='basic_left'><b> 2 - \u0110\u00fang<\/b>: <i> H\u00ecnh thang c\u0169ng l\u00e0 t\u1ee9 gi\u00e1c <\/i> n\u00ean m\u1ecdi t\u00ednh ch\u1ea5t c\u1ee7a t\u1ee9 gi\u00e1c th\u00ec c\u0169ng c\u00f3 \u1edf h\u00ecnh thang <br\/> <\/span>","<span class='basic_left'><b> 3 - Sai.<\/b> <\/span>"]}]}],"id_ques":1317},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","temp":"true_false","correct":[["f","f","f"]],"list":[{"point":5,"col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":[" Hai c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang lu\u00f4n song song v\u1edbi nhau "," Hai c\u1ea1nh \u0111\u00e1y c\u1ee7a h\u00ecnh thang lu\u00f4n c\u00f3 \u0111\u1ed9 d\u00e0i kh\u00e1c nhau"," M\u1ecdi t\u00ednh ch\u1ea5t c\u00f3 \u1edf h\u00ecnh thang vu\u00f4ng th\u00ec c\u0169ng c\u00f3 \u1edf h\u00ecnh thang c\u00e2n"],"explain":[" <span class='basic_left'><b> 1 - Sai<\/b>:<\/center> V\u00ec h\u00ecnh thang ch\u1ec9 c\u00f3 hai c\u1ea1nh b\u00ean song song khi h\u00ecnh thang \u0111\u00f3 c\u00f3 hai c\u1ea1nh \u0111\u00e1y b\u1eb1ng nhau. <br\/> <\/span> ","<span class='basic_left'><b> 2 - Sai<\/b>: V\u00ec hai c\u1ea1nh \u0111\u00e1y ch\u1ec9 b\u1eb1ng nhau khi h\u00ecnh thang c\u00f3 hai c\u1ea1nh b\u00ean song song. <br\/> <\/span>","<span class='basic_left'><b> 3 - Sai. <\/b> <\/span>"]}]}],"id_ques":1318},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Trong c\u00e1c h\u00ecnh sau, h\u00ecnh n\u00e0o l\u00e0 h\u00ecnh thang c\u00e2n? <\/span>","select":["A. <img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_5a.jpg' \/> ","B. <img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_5b.jpg' \/> ","C. <img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_5c.jpg' \/> "],"explain":" <span class='basic_left'> H\u00ecnh A l\u00e0 h\u00ecnh thang c\u00e2n. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":3}]}],"id_ques":1319},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t. <\/span>","select":["A. T\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y c\u1ee7a h\u00ecnh thang lu\u00f4n b\u1eb1ng $180^o$ ","B. T\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a m\u1ed9t h\u00ecnh thang lu\u00f4n b\u1eb1ng $180^o$ ","C. T\u1ed5ng hai g\u00f3c \u0111\u1ed1i c\u1ee7a m\u1ed9t h\u00ecnh thang lu\u00f4n b\u1eb1ng $180^o$ ","D. T\u1ed5ng hai g\u00f3c \u0111\u1ed1i c\u1ee7a m\u1ed9t h\u00ecnh thang lu\u00f4n b\u1eb1ng $90^o$ "],"explain":" <span class='basic_left'> T\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a m\u1ed9t h\u00ecnh thang lu\u00f4n b\u1eb1ng $180^o$. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":1}]}],"id_ques":1320},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC\\,(AB < AC)$, $AH$ l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a $\\Delta ABC$. C\u00e1c \u0111i\u1ec3m $D, E, F$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB, BC, AC$. Khi \u0111\u00f3 t\u1ee9 gi\u00e1c $DHEF$ l\u00e0 h\u00ecnh g\u00ec? <\/span>","select":["A. H\u00ecnh thang c\u00e2n ","B. H\u00ecnh thang vu\u00f4ng ","C. H\u00ecnh thang "],"explain":" <span class='basic_left'> V\u1ebd h\u00ecnh <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_6.jpg' \/><\/center> Theo b\u00e0i, $D, E, F$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB, BC$ v\u00e0 $AC$ n\u00ean: <br\/> $DF, DE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$. <br\/> $\\Rightarrow DF \/\/ BC$ <br\/> $ \\Rightarrow DF \/\/ HE$ <br\/> $\\Rightarrow DHEF$ l\u00e0 h\u00ecnh thang. (1) <br\/> Ta c\u00f3: $DE=\\dfrac{AC}{2}$ (2)<br\/> M\u1eb7t kh\u00e1c, v\u00ec $AH\\bot BC$ n\u00ean tam gi\u00e1c $AHC$ vu\u00f4ng t\u1ea1i $H$. <br\/>Suy ra, $HF=\\dfrac {AC}{2}$ (\u0110\u1ecbnh l\u00fd \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (3) <br\/>T\u1eeb (2) v\u00e0 (3), Suy ra $HF=DE$ (4)<br\/>T\u1eeb (1) v\u00e0 (4) $\\Rightarrow DHEF$ l\u00e0 h\u00ecnh thang c\u00e2n. (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A. <\/span><\/span> ","column":3}]}],"id_ques":1321},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho $\\Delta ABC$ c\u00e2n t\u1ea1i $A$. Tr\u00ean $AB, AC$ l\u1ea5y hai \u0111i\u1ec3m $M, N$ sao cho $BM = CN$. Bi\u1ebft $\\widehat{A}=100^o,$ khi \u0111\u00f3 $\\widehat {BMN}$ c\u00f3 s\u1ed1 \u0111o l\u00e0: <\/span>","select":["A. $40^o$ ","B. $80^o$ ","C. $100^o$ ","D. $140^o$ "],"hint":" T\u00ednh s\u1ed1 \u0111o g\u00f3c $AMN$, sau \u0111\u00f3 t\u00ednh g\u00f3c $BMN$.","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_7.jpg' \/><\/center> Theo \u0111\u1ec1 b\u00e0i, $BM = CN$. <br\/> L\u1ea1i c\u00f3 tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$. (gi\u1ea3 thi\u1ebft)$<br\/> \\Rightarrow AM = AN$ <br\/> Do \u0111\u00f3 $\\Delta AMN$ c\u00e2n t\u1ea1i $A$. <br\/> $\\Rightarrow \\widehat {AMN}=\\widehat {ANM}$ <br\/> M\u00e0 trong $\\Delta AMN$ c\u00f3: <br\/> $\\widehat{A}+\\widehat{AMN}+\\widehat{ANM}=180^o$ (\u0111\u1ecbnh l\u00ed t\u1ed5ng ba g\u00f3c trong tam gi\u00e1c)<br\/> $\\Rightarrow \\widehat {AMN}=\\widehat {ANM}=\\dfrac{180^o-\\widehat{A}}{2}=40^o$ <br\/> $\\Rightarrow \\widehat {AMN}=\\widehat {ANM}=\\dfrac{180^o-100^o}{2}=40^o$ <br\/> M\u00e0 $\\widehat{AMN}+ \\widehat{BMN}=180^o$ <br\/> $\\Rightarrow \\widehat {BMN}=180^o-\\widehat{AMN}$ $=180^o-40^o=140^o$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":1322},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho t\u1ee9 gi\u00e1c $MNPQ$ c\u00f3 $\\widehat{M}=125^o; \\widehat {N}=60^o; \\widehat{Q}=56^o$. T\u1ee9 gi\u00e1c $MNPQ$ l\u00e0 h\u00ecnh thang. <\/span> ","select":["\u0110\u00fang","Sai"],"hint":" Ki\u1ec3m tra xem t\u1ee9 gi\u00e1c $MNPQ$ c\u00f3 c\u1eb7p c\u1ea1nh \u0111\u1ed1i n\u00e0o song song kh\u00f4ng? T\u00ednh t\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh c\u00f3 b\u1eb1ng $180^o$ kh\u00f4ng? ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_8.jpg' \/><\/center> Ta x\u00e9t $\\widehat{M}+\\widehat {Q}=125^o+56^o=181^o$ <br\/> V\u00e0 $\\widehat{M}+\\widehat {N}=125^o+60^o=185^o$ <br\/> Do \u0111\u00f3 trong t\u1ee9 gi\u00e1c $MNPQ$ kh\u00f4ng c\u00f3 c\u1eb7p c\u1ea1nh n\u00e0o song song. <br\/> $\\Rightarrow MNPQ$ kh\u00f4ng l\u00e0 h\u00ecnh thang. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 Sai.<\/span>","column":2}]}],"id_ques":1323},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho t\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $\\widehat{B}=90^o; \\widehat {C}=95^o; \\widehat{D}=95^o$. T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh thang. <\/span> ","select":["\u0110\u00fang","Sai"],"hint":" Ki\u1ec3m tra xem t\u1ee9 gi\u00e1c $ABCD$ c\u00f3 c\u1eb7p c\u1ea1nh \u0111\u1ed1i n\u00e0o song song kh\u00f4ng? T\u00ednh t\u1ed5ng hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh c\u00f3 b\u1eb1ng $180^o$ kh\u00f4ng? ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_9.jpg' \/><\/center> Ta x\u00e9t $\\widehat{B}+\\widehat {C}=90^o+95^o=185^o$ <br\/> V\u00e0 $\\widehat{C}+\\widehat {D}=95^o+95^o=190^o$ <br\/> Do \u0111\u00f3 trong t\u1ee9 gi\u00e1c $ABCD$ kh\u00f4ng c\u00f3 c\u1eb7p c\u1ea1nh n\u00e0o song song <br\/> $\\Rightarrow ABCD$ kh\u00f4ng l\u00e0 h\u00ecnh thang. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 Sai.<\/span>","column":2}]}],"id_ques":1324},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho t\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $\\widehat{A}=100^o; \\widehat {C}=80^o; \\widehat {D}=80^o$. T\u1ee9 gi\u00e1c $ABCD$ l\u00e0 h\u00ecnh thang c\u00e2n. <\/span> ","select":["\u0110\u00fang","Sai"],"hint":" D\u1ef1a v\u00e0o d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft h\u00ecnh thang c\u00e2n. ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_10.jpg' \/><\/center> Ta x\u00e9t $\\widehat{A}+\\widehat {D}=100^o+80^o=180^o$ <br\/> $\\Rightarrow AB \/\/ CD$ <br\/> Do \u0111\u00f3 $ABCD$ l\u00e0 h\u00ecnh thang. <br\/> Trong h\u00ecnh thang $ABCD$ c\u00f3 $\\widehat {D}=\\widehat{C}=80^o$ <br\/> $\\Rightarrow ABCD$ l\u00e0 h\u00ecnh thang c\u00e2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft). <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":1325},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" <span class='basic_left'> Cho h\u00ecnh thang $ABCD$ nh\u01b0 h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_11.jpg' \/><\/center> Bi\u1ebft $\\widehat{B}=120^o$. T\u00ednh $\\widehat{C}$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{C} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o$ <\/span> ","hint":" Trong h\u00ecnh thang, hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u00f3 t\u1ed5ng b\u1eb1ng $180^o$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_11.jpg' \/><\/center> Do $ABCD$ l\u00e0 h\u00ecnh thang c\u00f3 hai \u0111\u00e1y l\u00e0 $AB$ v\u00e0 $CD$ n\u00ean: <br\/> $\\widehat{B}+\\widehat{C}=180^o$ <br\/> $\\Rightarrow \\widehat{C}=180^o-120^o=60^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $60$. <\/span><\/span> "}]}],"id_ques":1326},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" <span class='basic_left'> Cho h\u00ecnh thang c\u00e2n $MNPQ (MN \/\/ PQ)$ nh\u01b0 h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_12.jpg' \/><\/center> Bi\u1ebft $\\widehat{M}=140^o$. T\u00ednh $\\widehat{P}$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{P} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o$ <\/span> ","hint":" Trong h\u00ecnh thang, hai g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean c\u00f3 t\u1ed5ng b\u1eb1ng $180^o$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_12.jpg' \/><\/center> Do $MNPQ$ l\u00e0 h\u00ecnh thang c\u00e2n c\u00f3 hai \u0111\u00e1y l\u00e0 $MN$ v\u00e0 $PQ$ n\u00ean: <br\/> $\\widehat{M}+\\widehat{Q}=180^o$ <br\/> $\\Rightarrow \\widehat{Q}=180^o-140^o=40^o$ <br\/> M\u00e0 $MNPQ$ l\u00e0 h\u00ecnh thang c\u00e2n n\u00ean $\\widehat{P}=\\widehat{Q}$ <br\/> $\\Rightarrow \\widehat{P}=40^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $40$. <\/span><\/span> "}]}],"id_ques":1327},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["75"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" <span class='basic_left'> Cho h\u00ecnh thang c\u00e2n $EFGH\\, (EF \/\/ GH)$ nh\u01b0 h\u00ecnh sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_13.jpg' \/><\/center> Bi\u1ebft $\\widehat{E}=105^o$. T\u00ednh $\\widehat{F_1}$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $\\widehat{F_1} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o$ <\/span> ","hint":" D\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t h\u00ecnh thang c\u00e2n \u0111\u1ec3 t\u00ecm $\\widehat{F_1}$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_13.jpg' \/><\/center> Do $EFGH$ l\u00e0 h\u00ecnh thang c\u00e2n v\u1edbi hai \u0111\u00e1y l\u00e0 $EF$ v\u00e0 $GH$ n\u00ean: <br\/> $ \\widehat{E}=\\widehat{EFG}$ (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow \\widehat {EFG}=105^o$ <br\/> M\u00e0 $ \\widehat{EFG}+\\widehat{F_1}=180^o$ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> $\\widehat{F_1}=180^o-105^o=75^o$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $75$. <\/span><\/span> "}]}],"id_ques":1328},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["22"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" <span class='basic_left'> H\u00ecnh thang c\u00e2n $ABCD\\, (AB \/\/ CD, AB > CD)$, $BD$ l\u00e0 ph\u00e2n gi\u00e1c g\u00f3c $B$. Hai \u0111\u00e1y c\u00f3 \u0111\u1ed9 d\u00e0i $5\\, cm$ v\u00e0 $7 \\,cm$. Chu vi h\u00ecnh thang c\u00e2n $ABCD$ l\u00e0 _input_ $(cm)$<\/span> ","hint":" T\u00ecm \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang c\u00e2n $ABCD$.","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_14.jpg' \/><\/center> Theo b\u00e0i, ta c\u00f3: $\\widehat{B_1}=\\widehat{B_2}$ <br\/> M\u00e0 $\\widehat{B_2}=\\widehat{D_1}$ (so le trong) n\u00ean $\\widehat{B_1}=\\widehat{D_1}$ <br\/> Suy ra $\\Delta BCD$ c\u00e2n t\u1ea1i $C$. <br\/> $\\Rightarrow CD = BC = 5\\, (cm)$ <br\/> Chu vi c\u1ee7a h\u00ecnh thang c\u00e2n $ABCD$ l\u00e0: <br\/> $AB+BC+CD+AD=7+5+5+5=22\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $22$. <\/span><\/span> "}]}],"id_ques":1329},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> H\u00ecnh thang $ABCD\\, (AB < CD)$ vu\u00f4ng t\u1ea1i $A$ v\u00e0 $D$, hi\u1ec7u hai \u0111\u00e1y b\u1eb1ng $4\\, cm$, c\u1ea1nh b\u00ean $BC$ l\u00e0 $6\\, cm$. \u0110\u1ed9 \u0111\u00e0i c\u1ea1nh $AD$ l\u00e0: <\/span>","select":["A. $\\sqrt{52}\\, cm$ ","B. $\\sqrt{20}\\, cm$ ","C. $\\sqrt{50}\\, cm$ ","D. $2\\, cm$ "],"hint":" K\u1ebb $BE\\bot CD$ t\u1ea1i $E$, t\u00ednh \u0111\u1ed9 d\u00e0i $BE$ r\u1ed3i suy ra \u0111\u1ed9 d\u00e0i $AD$. ","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai2/lv1/img\/H812_D1_15.jpg' \/><\/center> K\u1ebb $BE\\bot CD$ t\u1ea1i $E$ $\\Rightarrow AB=DE; AD = BE$ (t\u00ednh ch\u1ea5t \u0111o\u1ea1n ch\u1eafn) <br\/> \u0110\u1eb7t $AB=DE=x$ <br\/> M\u00e0 $DC-AB=4$ hay $EC=4$ cm <br\/> X\u00e9t trong $\\Delta BCE$ vu\u00f4ng t\u1ea1i $E$:<br\/> $BC^2=BE^2+EC^2$ (\u0110\u1ecbnh l\u00fd Py - ta - go) <br\/> $\\Rightarrow BE^2=BC^2-EC^2$$=6^2-4^2=20$ <br\/> $\\Rightarrow BE=\\sqrt{20}$ (cm) <br\/> $\\Rightarrow AD = \\sqrt{20}$ (cm) <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":1330}],"lesson":{"save":0,"level":1}}