Quan hệ giữa ba cạnh của một tam giác. Bất đẳng thức tam giác-level1

Home Lớp 7 Toán lớp 7 - Sách kết nối tri thức Quan hệ giữa ba cạnh của một tam giác. Bất đẳng thức tam giácBài tập cơ bản

{"common":{"save":0,"post_id":"1343","level":1,"total":20,"point":5,"point_extra":0},"segment":[{"id":"1861","post_id":"1343","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":5,"ques":"V\u1edbi b\u1ed9 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 s\u1ed1 \u0111o sau \u0111\u00e2y, b\u1ed9 ba n\u00e0o kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c?","select":[" A. $3cm; 4cm; 5cm$ "," B. $2cm; 4cm; 6cm$ ","C. $6cm; 9cm; 12cm$ ","D. $5cm; 8cm; 10cm$ "],"hint":"S\u1eed d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c \u0111\u1ec3 ki\u1ec3m tra","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Trong tr\u01b0\u1eddng h\u1ee3p x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c $a$ l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t trong ba s\u1ed1 $a, b, c$ th\u00ec \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 t\u1ed3n t\u1ea1i tam gi\u00e1c ch\u1ec9 c\u1ea7n: $a <br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> +) Ta c\u00f3: <br\/> $5 < 3 + 4$ <br\/> N\u00ean b\u1ed9 ba s\u1ed1 $3cm; 4cm; 5cm$ c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c <br\/> +) $6 = 2 + 4$ <br\/> N\u00ean b\u1ed9 ba s\u1ed1 $2cm; 4cm; 6cm$ kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c <br\/> +) $12 < 6 + 9$ <br\/> N\u00ean b\u1ed9 ba s\u1ed1 $6cm; 9cm; 12cm$ c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c <br\/> +) $10 < 5 + 8$ <br\/> N\u00ean b\u1ed9 ba s\u1ed1 $5cm; 8cm; 10cm$ c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span> <br\/> Nh\u1eadn x\u00e9t: <br\/> +) Khi x\u00e9t \u0111\u1ed9 d\u00e0i ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 th\u1ecfa m\u00e3n b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c kh\u00f4ng ta, ch\u1ec9 c\u1ea7n so s\u00e1nh \u0111\u1ed9 d\u00e0i l\u1edbn nh\u1ea5t v\u1edbi t\u1ed5ng hai \u0111\u1ed9 d\u00e0i c\u00f2n l\u1ea1i <br\/> +) K\u1ebft qu\u1ea3 tr\u00ean c\u00f3 \u0111\u01b0\u1ee3c nh\u1edd v\u00e0o m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c \u0111\u1ec3 ch\u1ee9ng minh b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c, c\u1ee5 th\u1ec3: <br\/> <center><img src='img\/H7C3B19_D07.png' \/><\/center> <br\/> Trong $\\triangle{ABC}$ gi\u1ea3 s\u1eed $BC$ l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t suy ra $\\widehat{A}$ l\u1edbn nh\u1ea5t <br\/> K\u1ebb $AH \\perp BC$ ($H \\in BC$), ta c\u00f3: <br\/> - Trong $\\triangle{HAB}$ vu\u00f4ng t\u1ea1i $H$, ta c\u00f3: $BH < AB$ (1) <br\/> - Trong $\\triangle{HAC}$ vu\u00f4ng t\u1ea1i $H$, ta c\u00f3: $CH < AC$ (2) <br\/> C\u1ed9ng theo v\u1ebf c\u1ee7a (1) v\u00e0 (2), ta \u0111\u01b0\u1ee3c: <br\/> $BH + CH < AB + AC$ hay $BC < AB + AC$ <br\/> V\u1edbi gi\u1ea3 s\u1eed $BC$ l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t, n\u00ean c\u00e1c b\u1ea5t \u0111\u1eb3ng th\u1ee9c c\u00f2n l\u1ea1i l\u00e0 hi\u1ec3n nhi\u00ean <\/i> <\/span> ","column":2}]}]},"correct":"","level":"1","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:05"},{"id":"1862","post_id":"1343","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":[[1]],"list":[{"point":5,"ques":"T\u1ed3n t\u1ea1i m\u1ed9t tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh l\u00e0 $8m, 12m, 7m$. \u0110\u00fang <\/b> hay sai <\/b>?","select":[" A. \u0110\u00daNG "," B. SAI "],"hint":"","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Trong tr\u01b0\u1eddng h\u1ee3p x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c $a$ l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t trong ba s\u1ed1 $a, b, c$ th\u00ec \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 t\u1ed3n t\u1ea1i tam gi\u00e1c ch\u1ec9 c\u1ea7n: $a <br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> +) Ta c\u00f3: <br\/> $12 < 7 + 8 $ <br\/> N\u00ean b\u1ed9 ba s\u1ed1 $8m, 12m, 7m$ c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00daNG <\/span> <br\/> Nh\u1eadn x\u00e9t: Ngo\u00e0i c\u00e1ch tr\u00ean \u0111\u1ec3 x\u00e9t \u0111\u1ed9 d\u00e0i ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 th\u1ecfa m\u00e3n b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c hay kh\u00f4ng ta c\u00f3 th\u1ec3 so s\u00e1nh \u0111\u1ed9 d\u00e0i nh\u1ecf nh\u1ea5t v\u1edbi hi\u1ec7u hai \u0111\u1ed9 d\u00e0i c\u00f2n l\u1ea1i <br\/> Trong tr\u01b0\u1eddng h\u1ee3p x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c $a$ l\u00e0 s\u1ed1 nh\u1ecf nh\u1ea5t trong $3$ s\u1ed1 th\u00ec \u0111i\u1ec1u ki\u1ec7n t\u1ed3n t\u1ea1i tam gi\u00e1c ch\u1ec9 c\u1ea7n $a > |b - c|$ <\/i> <\/span> ","column":2}]}]},"correct":"","level":"1","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:05"},{"id":"1863","post_id":"1343","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":[[4]],"list":[{"point":5,"ques":"\u0110\u1ed9 d\u00e0i hai c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 $4cm$ v\u00e0 $12cm$. Trong c\u00e1c s\u1ed1 \u0111o sau \u0111\u00e2y, s\u1ed1 \u0111o n\u00e0o l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a tam gi\u00e1c \u0111\u00f3? ","select":[" A. $6cm$ "," B. $7cm$ ","C. $8cm$","D. $9cm$"],"hint":"\u00c1p d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c cho c\u00e1c b\u1ed9 ba s\u1ed1 \u0111o \u0111\u1ed9 d\u00e0i","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Trong tr\u01b0\u1eddng h\u1ee3p x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c $a$ l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t trong ba s\u1ed1 $a, b, c$ th\u00ec \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 t\u1ed3n t\u1ea1i tam gi\u00e1c ch\u1ec9 c\u1ea7n: $a <br\/><br\/> B\u00e0i gi\u1ea3i:<\/span><br\/> \u00c1p d\u1ee5ng b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c, ta c\u00f3: <br\/> +) $12 > 6 + 4 $ <br\/> N\u00ean $6cm$ kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a tam gi\u00e1c <br\/> +) $12 > 4 + 7$ <br\/> N\u00ean $7cm$ kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a tam gi\u00e1c <br\/> +) $12 = 8 + 4$ <br\/> N\u00ean $8cm$ kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a tam gi\u00e1c <br\/> +) $12 < 9 + 4$ <br\/> N\u00ean $9cm$ c\u00f3 th\u1ec3 l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a tam gi\u00e1c <br\/> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: D <\/span> ","column":2}]}]},"correct":"","level":"1","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:23:05"}]}