Quan hệ giữa góc và cạnh đối diện trong một tam giác level3

Home Lớp 7 Toán lớp 7 - Sách kết nối tri thức Quan hệ giữa góc và cạnh đối diện trong một tam giácBài tập nâng cao

{"common":{"save":0,"post_id":"1332","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"1821","post_id":"1332","mon_id":"0","chapter_id":"0","question":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","options":{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $MIK$ c\u00f3 $MI < MK$. G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $IK$. <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. $\\widehat{IMH} = \\widehat{HMK}$ ","B. $\\widehat{IMH} > \\widehat{HMK}$","C. $\\widehat{IMH} < \\widehat{HMK}$"],"hint":"V\u1ebd th\u00eam \u0111i\u1ec3m $D$ sao cho $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MD$","explain":" H\u01b0\u1edbng d\u1eabn:<\/span><br\/> B\u01b0\u1edbc 1: <\/b> V\u1ebd th\u00eam \u0111i\u1ec3m $D$ sao cho $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MD$ <br\/> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $\\widehat{M_{1}}$ v\u00e0 $\\widehat{D}$ b\u1eb1ng c\u00e1ch ch\u1ee9ng minh $\\triangle{IHM} = \\triangle{KHD}$ <br\/> B\u01b0\u1edbc 3: <\/b> So s\u00e1nh $\\widehat{D}$ v\u00e0 $\\widehat{M_{2}}$ b\u1eb1ng c\u00e1ch so s\u00e1nh $MK$ v\u00e0 $KD$ <br\/> B\u01b0\u1edbc 4: <\/b> So s\u00e1nh $\\widehat{M_{1}}$ v\u00e0 $\\widehat{M_{2}}$ <br\/><br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='img\/H7C3B17_TB01.png' \/><\/center> <br\/> V\u1ebd \u0111i\u1ec3m $D$ sao cho $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MD$ <br\/> X\u00e9t $\\triangle{IHM} = \\triangle{KHD}$ c\u00f3: <br\/> $\\begin{cases} IH = HK (gt) \\\\ \\widehat{IHM} = \\widehat{KHD} (\\text{\u0111\u1ed1i} \\hspace{0,2cm} \\text{\u0111\u1ec9nh}) \\\\ MH = HD (\\text{c\u00e1ch} \\hspace{0,2cm} \\text{v\u1ebd}) \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{IHM} = \\triangle{KHD}$ (c. g. c) <br\/> $\\Rightarrow$ $\\widehat{M_{1}} = \\widehat{D}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) (1) <br\/> V\u00e0 $IM = KD$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) (2) <br\/> M\u1eb7t kh\u00e1c ta c\u00f3: $MI < MK$ (gt) (3) <br\/> T\u1eeb (2) v\u00e0 (3) $\\Rightarrow$ $KD < MK$ <br\/> $\\Rightarrow$ $\\widehat{M_{2}} < \\widehat{D}$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong tam gi\u00e1c $KMD$) (4) <br\/> T\u1eeb (1) v\u00e0 (4) $\\Rightarrow \\widehat{M_{2}} < \\widehat{M_{1}}$ hay $\\widehat{IMH} > \\widehat{HMK}$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span> ","column":3}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:04"},{"id":"1822","post_id":"1332","mon_id":"0","chapter_id":"0","question":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","options":{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $MNP$ vu\u00f4ng t\u1ea1i $M$, tia ph\u00e2n gi\u00e1c g\u00f3c $N$ c\u1eaft $MP$ \u1edf $I$. <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. $MI = IP$ ","B. $MI > IP$","C. $MI < IP$"],"hint":"K\u1ebb $IH$ vu\u00f4ng g\u00f3c v\u1edbi $NP$ ","explain":" H\u01b0\u1edbng d\u1eabn:<\/span><br\/> B\u01b0\u1edbc 1: <\/b> K\u1ebb $IH$ vu\u00f4ng g\u00f3c v\u00f3i $NP$ sau \u0111\u00f3 so s\u00e1nh $IM$ v\u00e0 $IH$ <br\/> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $IH$ v\u00e0 $IP$ <br\/> B\u01b0\u1edbc 3: <\/b> So s\u00e1nh $IM$ v\u00e0 $IP$ <br\/><br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='img\/H7C3B17_TB02.png' \/><\/center> <br\/>K\u1ebb $IH$ vu\u00f4ng g\u00f3c v\u1edbi $NP$ <br\/> X\u00e9t $\\triangle{NMI}$ v\u00e0 $\\triangle{NHI}$ c\u00f3: <br\/> $\\begin{cases} \\widehat{NMI} = \\widehat{NHI} = 90^{o} \\\\ \\text{C\u1ea1nh} \\hspace{0,2cm} IN \\hspace{0,2cm} \\text{chung} \\\\ \\widehat{MNI} = \\widehat{HNI} (gt) \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{NMI} = \\triangle{NHI}$ (g.c.g) <br\/> $\\Rightarrow$ $IM = IH$ (c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) (1) <br\/> Trong $\\triangle{IHP}$ c\u00f3: <br\/> $\\widehat{IHP} = 90^{o}$ (c\u00e1ch l\u1ea5y \u0111i\u1ec3m $H$) <br\/> $\\Rightarrow$ $IH < IP$ (trong tam gi\u00e1c vu\u00f4ng c\u1ea1nh huy\u1ec1n l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $IM < IP$ <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> <br\/> Nh\u1eadn x\u00e9t: \u1ede b\u00e0i n\u00e0y ta ph\u1ea3i so s\u00e1nh $MI$ v\u00e0 $IP$ kh\u00f4ng ph\u1ea3i l\u00e0 hai c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c n\u00ean kh\u00f4ng v\u1eadn d\u1ee5ng \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00fd v\u1ec1 quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong m\u1ed9t tam gi\u00e1c. Ta chuy\u1ec3n $MI$ v\u00e0 $IP$ v\u1ec1 c\u00f9ng m\u1ed9t tam gi\u00e1c b\u1eb1ng c\u00e1ch v\u1ebd th\u00eam \u0111\u01b0\u1eddng ph\u1ee5 $IH$. L\u00fac \u0111\u00f3 $MI = IH$, ta ch\u1ec9 c\u00f2n ph\u1ea3i so s\u00e1nh $MI$ v\u00e0 $IP$ \u1edf c\u00f9ng m\u1ed9t tam gi\u00e1c <\/i> <\/span> ","column":3}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:04"},{"id":"1823","post_id":"1332","mon_id":"0","chapter_id":"0","question":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","options":{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $KHL$ c\u00f3 $KH < KL$, tia ph\u00e2n gi\u00e1c g\u00f3c $K$ c\u1eaft $HL$ \u1edf $D$. <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. $HD = DL$ ","B. $HD > DL$","C. $HD < DL$"],"hint":"Tr\u00ean $HL$ l\u1ea5y \u0111i\u1ec3m $I$ sao cho $KH = KI$ ","explain":" H\u01b0\u1edbng d\u1eabn:<\/span><br\/> B\u01b0\u1edbc 1: <\/b> Tr\u00ean $KL$ l\u1ea5y \u0111i\u1ec3m $I$ sao cho $KH = KI$ <br\/> Sau \u0111\u00f3 so s\u00e1nh $HD$ v\u00e0 $ID$ <br\/> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $\\widehat{H_{1}}$ v\u00e0 $\\widehat{I_{1}}$ <br\/> B\u01b0\u1edbc 3: <\/b> So s\u00e1nh $\\widehat{H_{1}}$ v\u00e0 $\\widehat{L}$ <br\/> B\u01b0\u1edbc 4: <\/b> So s\u00e1nh $\\widehat{I_{1}}$ v\u00e0 $\\widehat{L}$ t\u1eeb \u0111\u00f3 so s\u00e1nh \u0111\u01b0\u1ee3c $HD$ v\u00e0 $DL$ <br\/><br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='img\/H7C3B17_TB03.png' \/><\/center> <br\/> Tr\u00ean $KL$ l\u1ea5y \u0111i\u1ec3m $I$ sao cho $KH = KI$ <br\/> X\u00e9t $\\triangle{KHD}$ v\u00e0 $\\triangle{KID}$ c\u00f3: <br\/> $\\begin{cases} KH = KI (\\text{c\u00e1ch} \\hspace{0,2cm} \\text{l\u1ea5y} \\hspace{0,2cm} \\text{\u0111i\u1ec3m} \\hspace{0,2cm} I) \\\\ \\widehat{HKD} = \\widehat{IKD} (gt) \\\\ \\text{C\u1ea1nh} \\hspace{0,2cm} KD \\hspace{0,2cm} \\text{chung} \\end{cases}$ <br\/> $\\Rightarrow$ $\\triangle{HKD} = \\triangle{IKD}$ (c. g . c) <br\/> $\\Rightarrow$ $HD = ID$ (c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) (1) <br\/> Ta c\u00f3: $\\widehat{H_{1}}$ l\u00e0 g\u00f3c ngo\u00e0i t\u1ea1i $H$ c\u1ee7a tam gi\u00e1c $HKD$ n\u00ean: $\\widehat{H_{1}} = \\widehat{HDK} + \\widehat{HKD}$ <br\/> $\\widehat{I_{1}}$ l\u00e0 g\u00f3c ngo\u00e0i t\u1ea1i $I$ c\u1ee7a tam gi\u00e1c $KID$ n\u00ean: $\\widehat{I_{1}} = \\widehat{IDK} + \\widehat{IKD}$ <br\/> M\u00e0 $\\widehat{HDK} = \\widehat{IDK}$ (v\u00ec $\\triangle{HDK} = \\triangle{IDK}$) <br\/> $\\widehat{HKD} = \\widehat{IKD}$ (gt) <br\/> N\u00ean: $\\widehat{H_{1}} = \\widehat{I_{1}}$ (2) <br\/> M\u1eb7t kh\u00e1c: $\\widehat{H_{1}}$ l\u00e0 g\u00f3c ngo\u00e0i t\u1ea1i $H$ c\u1ee7a tam gi\u00e1c $HKL$ n\u00ean $\\widehat{H_{1}} > \\widehat{L}$ (3) <br\/> T\u1eeb (2) v\u00e0 (3) $\\Rightarrow$ $\\widehat{I_{1}} > \\widehat{L}$ <br\/> X\u00e9t $\\triangle{DIL}$ c\u00f3 $\\widehat{I_{1}} >\\widehat{L}$ <br\/> N\u00ean $DL > DI$ (\u0111\u1ecbnh l\u00fd quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong tam gi\u00e1c) (4) <br\/> T\u1eeb (1) v\u00e0 (4) $\\Rightarrow$ $HD < DL$ <br\/> <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C <\/span> <br\/> Nh\u1eadn x\u00e9t: +) Sai l\u1ea7m c\u00f3 th\u1ec3 m\u1eafc ph\u1ea3i l\u00e0 t\u01b0\u1edfng r\u1eb1ng $\\widehat{HKD} = \\widehat{DKL}$ th\u00ec $HD = DL$ <br\/> +) L\u01b0u \u00fd r\u1eb1ng \u0111\u1ec3 so s\u00e1nh hai \u0111o\u1ea1n th\u1eb3ng n\u00ean \u0111\u01b0a v\u1ec1 c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c \u0111\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd v\u1ec1 quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong m\u1ed9t tam gi\u00e1c. <br\/> +) Ngo\u00e0i ra \u1edf b\u00e0i n\u00e0y c\u00f2n s\u1eed d\u1ee5ng quan h\u1ec7 gi\u1eefa g\u00f3c ngo\u00e0i c\u1ee7a tam gi\u00e1c v\u1edbi g\u00f3c trong kh\u00f4ng k\u1ec1 \u0111\u1ec3 so s\u00e1nh g\u00f3c <\/i> <\/span> ","column":3}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:04"}]}