{"segment":[{"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'> Ph\u00e1t bi\u1ec3u c\u1ee7a \u0111\u1ecbnh l\u00ed Py-ta-go l\u00e0: <br\/> ''Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a c\u1ea1nh huy\u1ec1n b\u1eb1ng <br\/> t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng.'' ","select":["\u0110\u00fang","Sai"],"hint":"","explain":"Ph\u00e1t bi\u1ec3u tr\u00ean l\u00e0 \u0110\u00fang.","column":2}]}],"id_ques":1701},{"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":"","select":["A. N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh kia th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c nh\u1ecdn. ","B. N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh kia th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c vu\u00f4ng. ","C. N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh kia th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c t\u00f9. ","D. N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh kia th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c c\u00e2n. "],"hint":"","explain":" <span class='basic_left'> <span class='basic_pink'>Ph\u00e1t bi\u1ec3u \u0111\u00fang l\u00e0 B <\/span> <br\/> Ta c\u00f3 \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o: <br\/> ''N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai c\u1ea1nh kia th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c vu\u00f4ng.'' ","column":1}]}],"id_ques":1702},{"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":" <b> T\u00ecm c\u00e2u tr\u1ea3 l\u1eddi sai <\/b> <br\/> Tam gi\u00e1c $DHK$ vu\u00f4ng t\u1ea1i $D$ khi: ","select":["A. $\\widehat{H} + \\widehat{K} = 90^{o} $","B. $DH^{2} + DK^{2} = HK^{2} $","C. $\\widehat{D} = \\widehat{H} + \\widehat{K} $ ","D. $DH^{2} + HK^{2} = DK^{2} $ "],"hint":"V\u1ebd h\u00ecnh r\u1ed3i t\u00ecm ra \u0111\u00e1p \u00e1n. ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-01.png' \/><\/center> <span class='basic_left'> Ta c\u00f3 $\\triangle DHK $ vu\u00f4ng t\u1ea1i D n\u00ean: <br\/> A. $\\widehat{H} + \\widehat{K} = 90^{o} $ <br\/> B. Theo \u0111\u1ecbnh l\u00ed Py-ta-go c\u00f3: $DH^{2} + DK^{2} = HK^{2} $ <br\/> C. $\\widehat{D} = \\widehat{H} + \\widehat{K} = 90^{o}$ <br\/> C\u00e2u tr\u1ea3 l\u1eddi sai l\u00e0 D. ","column":2}]}],"id_ques":1703},{"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":" T\u00ecm c\u00e2u tr\u1ea3 l\u1eddi <b> SAI <\/b> <br\/> Cho tam gi\u00e1c $PQR$ vu\u00f4ng t\u1ea1i $P$. Khi \u0111\u00f3: ","select":["A. $QR > PQ $","B. $QR > PR $","C. $QR^{2} = PQ^{2} + PR^{2}$ ","D. $QR^{2} + PR^{2} = PQ^{2} $ "],"hint":"V\u1ebd h\u00ecnh r\u1ed3i t\u00ecm ra \u0111\u00e1p \u00e1n. ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-02.png' \/><\/center> <span class='basic_left'> $\\triangle PQR $ vu\u00f4ng t\u1ea1i P n\u00ean theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $QR^{2} = PQ^{2} + PR^{2}$ $\\Rightarrow $ c\u00e2u C \u0111\u00fang. <br\/> V\u00ec \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111o\u1ea1n th\u1eb3ng l\u00e0 m\u1ed9t s\u1ed1 d\u01b0\u01a1ng n\u00ean: <br\/> $QR > PQ, QR > PR $ <br\/> $\\Rightarrow $ c\u00e1c c\u00e2u A, B \u0111\u00fang . <br\/> C\u00e2u tr\u1ea3 l\u1eddi sai l\u00e0 D. ","column":2}]}],"id_ques":1704},{"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":" <b> T\u00ecm c\u00e2u tr\u1ea3 l\u1eddi sai<\/b> <br\/> Cho h\u00ecnh v\u1ebd bi\u1ebft $DE \/\/ HK$. Khi \u0111\u00f3: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-04.png' \/><\/center> ","select":["A. $DK = 10 $","B. $\\widehat{EDH} = 90^{o} $","C. $DK = 9$ ","D. $\\widehat{DHK} = 90^{o} $ "],"hint":"","explain":" <\/center> <span class='basic_left'> Ta c\u00f3 $DE \/\/ HK$ n\u00ean $\\widehat{EDH} = \\widehat{DHK} = 90^{o} $ (hai g\u00f3c so le trong) <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng $DHK$ ta \u0111\u01b0\u1ee3c: <br\/> $DK^{2} = DH^{2} + HK^{2} \\\\ \\Rightarrow DK^{2} = 8^{2} + (\\sqrt{17})^{2} \\\\ \\Rightarrow DK^{2} = 64 + 17 = 81 = 9^{2} \\\\ \\Rightarrow DK = 9 cm$ <br\/> <br\/> <span class='basic_pink'> C\u00e2u tr\u1ea3 l\u1eddi sai l\u00e0 A <\/span> ","column":2}]}],"id_ques":1705},{"time":9,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["13"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" T\u00ecm $x$ trong h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-05.png' \/> <\/center> <b> \u0110\u00e1p \u00e1n: <\/b> $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng ta \u0111\u01b0\u1ee3c: <br\/> $x^{2} = 12^{2} + 5^{2} \\\\ \\Leftrightarrow x^{2} = 144 + 25 \\\\ \\Leftrightarrow x^{2} = 169 = 13^{2} \\\\ \\Rightarrow x = 13 $ <\/span> "}]}],"id_ques":1706},{"time":9,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"]]],"list":[{"point":5,"width":40,"type_input":"","ques":" T\u00ecm $x$ trong h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y: <center> <img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-07.png' \/> <\/center> <b> \u0110\u00e1p \u00e1n: <\/b> $x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng ta \u0111\u01b0\u1ee3c: <br\/> $29^{2} = 21^{2} + x^{2} \\\\ \\Leftrightarrow x^{2} = 29^{2} - 21^{2} \\\\ \\Leftrightarrow x^{2} = 400 = 20^{2} \\\\ \\Rightarrow x = 20 $ <\/span> "}]}],"id_ques":1707},{"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'> Tam gi\u00e1c $ABC$ c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh $AB = 8 cm, AC = 17 cm, BC = 15 cm$. <br\/> Tam gi\u00e1c $ABC$ c\u00f3 ph\u1ea3i tam gi\u00e1c vu\u00f4ng kh\u00f4ng? ","select":["C\u00f3","Kh\u00f4ng"],"hint":"D\u1ef1a v\u00e0o \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o. ","explain":" <span class='basic_left'> Ta c\u00f3: $AB^{2} + BC^{2} = 8^{2} + 15^{2} = 64 + 225 = 289 (cm)\\\\ AC^{2} = 17^{2} = 289 (cm) $ <br\/> Do \u0111\u00f3, nh\u1eadn th\u1ea5y: $AB^{2} + BC^{2} = AC^{2} $ n\u00ean tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $B$ ","column":2}]}],"id_ques":1708},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\sqrt{8}$","B. $2\\sqrt{8}$","C. $3\\sqrt{8}$"],"ques":" <span class='basic_left'> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n c\u1ee7a m\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00e2n bi\u1ebft c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng 2dm. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b> ?(dm) ","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-12.png' \/><\/center> X\u00e9t $\\triangle ABC $ vu\u00f4ng c\u00e2n t\u1ea1i A. <br\/> $BC^{2} = 2^{2} + 2^{2} = 8 \\\\ \\Rightarrow BC = \\sqrt{8} \\, (dm) $ "}]}],"id_ques":1709},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\sqrt{2}$","B. $2\\sqrt{2}$","C. $3\\sqrt{2}$"],"ques":"<span class='basic_left'> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a m\u1ed9t tam gi\u00e1c ABC vu\u00f4ng c\u00e2n t\u1ea1i A. Bi\u1ebft c\u1ea1nh huy\u1ec1n b\u1eb1ng $2\\, m$. <br\/> <br\/> <b> \u0110\u00e1p \u00e1n: <\/b>AB = ?(m) ","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-13.png' \/><\/center> X\u00e9t $\\triangle ABC $ vu\u00f4ng c\u00e2n t\u1ea1i A. <br\/> $AB^{2} + AC^{2} = BC^{2} = 2^{2} = 4 \\\\ \\Rightarrow 2AB^{2} = 4 \\\\ \\Rightarrow AB^{2} = 2 \\\\ \\Rightarrow AB = \\sqrt{2}\\, (m) $ "}]}],"id_ques":1710},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $AD = \\sqrt{5}; BC = 5$","B. $AD = \\sqrt{5}; BC = 4$","C. $AD = \\sqrt{4}; BC = 5$"],"ques":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-23.png' \/><\/center> <br\/> T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng $AD, BC$ tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9. <br\/> (v\u1edbi \u0111\u01a1n v\u1ecb l\u00e0 \u0111\u01a1n v\u1ecb d\u00e0i c\u1ee7a h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9) <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $AD$ = ?; $BC$ = ?","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng $AOD$ ta \u0111\u01b0\u1ee3c: <br\/> $AD^{2} $$ = OA^{2} + OD^{2} \\\\ = 2^{2} + 1^{2} \\\\ = 5 $ <br\/> $\\Rightarrow AD = \\sqrt{5} $ <br\/> T\u01b0\u01a1ng t\u1ef1 ta c\u00f3: <br\/> $BC^{2} $$ = OB^{2} +OC^{2} \\\\ = 3^{2} + 4^{2} \\\\ = 25 = 5^{2} $ <br\/> $\\Rightarrow BC = 5$"}]}],"id_ques":1711},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $OA = \\sqrt{30}$","B. $OA = \\sqrt{32}$","C. $OA = \\sqrt{34}$"],"ques":" <span class='basic_left'> Tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, v\u1ebd \u0111i\u1ec3m A c\u00f3 t\u1ecda \u0111\u1ed9 (3; 5). <br\/> T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m A \u0111\u1ebfn g\u1ed1c t\u1ecda \u0111\u1ed9. <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-24.png' \/><\/center>","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'>Ta c\u00f3: $OA^{2} $$ = 3^{2} + 5^{2} \\\\ = 9 + 25 \\\\ = 34 $ <br\/> $\\Rightarrow OA = \\sqrt{34}$"}]}],"id_ques":1712},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $AB = \\sqrt{20}$","B. $AB = \\sqrt{24}$","C. $AB = \\sqrt{26}$"],"ques":"Cho h\u00ecnh v\u1ebd: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-28.png' \/><\/center> <br\/> T\u00ednh \u0111\u1ed9 d\u00e0i <b>$AB$<\/b>;<br\/><br\/>","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'> Ta c\u00f3: $AB^{2} $$ = 5^{2} + 1^{2} \\\\ = 25 + 1 \\\\ = 26 $ <br\/> $\\Rightarrow AB = \\sqrt{26} $"}]}],"id_ques":1713},{"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'> Cho tam gi\u00e1c $ABC$ bi\u1ebft $BC = 7,5cm; CA = 4,5cm; AB = 6cm.$ <br\/> \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao $AH$ c\u1ee7a $\\Delta ABC$ l\u00e0: ","select":["A. 12,96 cm","B. 6,48 cm ","C. 3,6 cm ","D. 6,3 cm "],"hint":" X\u00e9t xem tam gi\u00e1c $ABC$ l\u00e0 tam gi\u00e1c g\u00ec. ","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-31.png' \/><\/center> <span class='basic_left'> Ta c\u00f3: $BC^{2} = (7,5)^{2} = 56,25 \\\\ AC^{2} + AB^{2} = (4,5)^{2} + 6^{2} = 20,25 + 36 = 56,25 $ <br\/> Ta th\u1ea5y $BC^{2} = AC^{2} + AB^{2} $ <br\/> V\u1eady theo \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o: $\\triangle ABC $ l\u00e0 tam gi\u00e1c vu\u00f4ng t\u1ea1i A. <br\/> Ta l\u1ea1i c\u00f3: $AB.AC=AH.BC$ ($=2S_{ABC}$) <br\/> Thay s\u1ed1: $6.4,5=AH.7,5$ <br\/> $\\Rightarrow AH=\\dfrac{6.4,5}{7,5}$ <br\/> $\\Rightarrow AH=3,6\\, (cm)$ <br\/><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> ","column":4}]}],"id_ques":1714},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"],["13"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":["sqrt"],"ques":" <span class='basic_left'> Cho tam gi\u00e1c $ABC$ c\u00f3 c\u00e1c g\u00f3c B, C nh\u1ecdn. K\u1ebb $AH \\perp BC $. <br\/> Bi\u1ebft AB = 20cm, BH = 16cm, HC = 5cm. <br\/> T\u00ednh \u0111\u1ed9 d\u00e0i $AH; AC$. <br\/><br\/> <b> \u0110\u00e1p \u00e1n: <\/b> $ AH$ = _input_ (cm); $AC$ = _input_ (cm)","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-36.png' \/><\/center> <span class='basic_left'>Tam gi\u00e1c $ABH$ vu\u00f4ng t\u1ea1i H n\u00ean theo \u0111\u1ecbnh l\u00ed Py-ta-go, ta c\u00f3: <br\/> $AH^{2} $$ = AB^{2} - BH^{2} \\\\ = 20^{2} - 16^{2} \\\\ = 144 = 12^{2} $ <br\/> $\\Rightarrow AH = 12 (cm) $ <br\/> Tam gi\u00e1c $AHC$ vu\u00f4ng t\u1ea1i H n\u00ean theo \u0111\u1ecbnh l\u00ed Py-ta-go, ta c\u00f3: <br\/> $AC^{2} $$ = AH^{2} + HC^{2} \\\\ = 12^{2} + 5^{2} \\\\ = 169 = 13^{2} $ <br\/> $\\Rightarrow AC = 13 (cm) $"}]}],"id_ques":1715},{"time":9,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1"]],"list":[{"point":5,"ques":"Tam gi\u00e1c n\u00e0o l\u00e0 tam gi\u00e1c vu\u00f4ng trong c\u00e1c tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh nh\u01b0 sau: ","hint":"","column":3,"number_true":1,"select":["6cm, 10cm, 8cm","6cm, 9cm, 11cm","4m, 8m, 9m"],"explain":" <span class='basic_left'> a) $6^{2} = 36; 10^{2} = 100, 8^{2} = 64 $ <br\/> Ta th\u1ea5y: 36 + 64 = 100 n\u00ean \u0111\u00e2y l\u00e0 tam gi\u00e1c vu\u00f4ng theo \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o. <br\/> b) $6^{2} = 36; 9^{2} = 81; 11^{2} = 121 $ <br\/> Ta th\u1ea5y: $ 36 + 81 \\neq 121 $ n\u00ean kh\u00f4ng t\u1ed3n t\u1ea1i tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh nh\u01b0 tr\u00ean. <br\/> c) $4^{2} = 16; 8^{2} = 64, 9^{2} = 81 $ <br\/> Ta th\u1ea5y: 81 $\\neq $ 16 + 64 n\u00ean kh\u00f4ng t\u1ed3n t\u1ea1i tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i ba c\u1ea1nh nh\u01b0 tr\u00ean. "}]}],"id_ques":1716},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["20","48"],["48","20"]]],"list":[{"point":5,"width":20,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00f3 c\u1ea1nh huy\u1ec1n b\u1eb1ng 52cm, \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh g\u00f3c vu\u00f4ng t\u1ec9 l\u1ec7 v\u1edbi 5 v\u00e0 12. <br\/> T\u00ednh \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng? <br\/> <br\/> <b> \u0110\u00e1p \u00e1n:<\/b> $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}(cm); \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}(cm)$<\/span> ","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng.","explain":" <span class='basic_left'> G\u1ecdi a v\u00e0 b l\u00e0 \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng (cm) $(a, b > 0)$ <br\/> Theo b\u00e0i ta c\u00f3: $\\dfrac{a}{5} = \\dfrac{b}{12} \\\\ \\Rightarrow \\dfrac{a^{2}}{25} = \\dfrac{b^{2}}{144} = \\dfrac{a^{2}+b^{2}}{25+144} = \\dfrac{52^{2}}{169} = 16 $ <br\/> Do \u0111\u00f3: $\\left( \\dfrac{a}{5} \\right)^{2} = \\left( \\dfrac{b}{12} \\right)^{2} = 4^{2} $ <br\/> Suy ra: $\\dfrac{a}{5} = \\dfrac{b}{12} = 4 $ <br\/> V\u1eady $a = 5.4 = 20 (cm) \\\\ b = 12.4 = 48 (cm)$ <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 20 v\u00e0 48 ho\u1eb7c 48 v\u00e0 20<\/span> <\/span>. "}]}],"id_ques":1717},{"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'> Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i B, bi\u1ebft: $AB = 17cm, AC = 16cm.$ <br\/> G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC, \u0111\u1ed9 d\u00e0i $BM$ l\u00e0: ","select":["A. 12 cm ","B. 15 cm ","C. 13 cm ","D. 11 cm "],"hint":"X\u00e9t xem tam gi\u00e1c $AMB$ l\u00e0 tam gi\u00e1c g\u00ec. ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Ch\u1ee9ng minh $\\triangle ABM = \\triangle CBM $ <br\/> <b>B\u01b0\u1edbc 2: <\/b> Ch\u1ee9ng minh tam gi\u00e1c $AMB$ vu\u00f4ng t\u1ea1i M. <br\/> <b> B\u01b0\u1edbc 3: <\/b> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh BM. <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-37.png' \/><\/center> X\u00e9t $\\triangle ABM $ v\u00e0 $\\triangle CBM $ c\u00f3: <br\/> + $AB = CB$ ($\\triangle ABC $ c\u00e2n t\u1ea1i B) <br\/> + c\u1ea1nh BM chung <br\/> + $AM = CM=\\dfrac{AC}{2}=8\\,(cm)$ (M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC) <br\/> Do \u0111\u00f3 $\\triangle ABM = \\triangle CBM (c.c.c) $ <br\/> $\\Rightarrow \\widehat{M_{1}} = \\widehat{M_{2}} $ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> M\u00e0 $\\widehat{M_{1}} + \\widehat{M_{2}} = 180^{o} $ (k\u1ec1 b\u00f9) <br\/> $\\Rightarrow 2\\widehat{M_{1}} = 180^{o} \\Rightarrow \\widehat{M_{1}} = 90^{o} $ <br\/> $\\Rightarrow \\triangle AMB $ vu\u00f4ng t\u1ea1i M. <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go cho tam gi\u00e1c vu\u00f4ng $AMB$ ta \u0111\u01b0\u1ee3c: <br\/> $BM^{2} $$ = AB^{2} - AM^{2} \\\\ = 17^{2} - 8^{2} \\\\ = 225 = 15^{2} $ <br\/> $\\Rightarrow BM = 15 cm $<br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span> ","column":4}]}],"id_ques":1718},{"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 tam gi\u00e1c $ABC$, bi\u1ebft: $BC = 52cm, AB = 20cm, AC = 48cm.$ <br\/> Khi \u0111\u00f3 $\\triangle ABC $ vu\u00f4ng t\u1ea1i ","select":["A ","B ","C"],"hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o ","explain":" <span class='basic_left'> Ta c\u00f3: $BC^{2} = 52^{2} = 2704 \\\\ AB^{2} = 20^{2} = 400 \\\\ AC^{2} = 48^{2} = 2304$ <br\/> Nh\u1eadn th\u1ea5y $2304 + 400 = 2704$ <br\/> hay $AC^{2} + AB^{2} = BC^{2} $ <br\/> Theo \u0111\u1ecbnh l\u00ed Py-ta-go \u0111\u1ea3o th\u00ec tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i A. ","column":3}]}],"id_ques":1719},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"select":["A. $BC = \\sqrt{300}$","B. $BC = \\sqrt{304}$","C. $BC = \\sqrt{306}$"],"ques":"Cho $\\triangle ABC $ c\u00e2n t\u1ea1i A bi\u1ebft $AB = AC = 17cm$.<br\/>K\u1ebb $BD \\perp AC $. Bi\u1ebft $BD = 15cm$. T\u00ednh c\u1ea1nh \u0111\u00e1y BC. =?(cm) ","hint":"T\u00ednh $AD, DC, BC.$ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh c\u1ea1nh $AD$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh $CD = AC - AD$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh $BC$ <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai14/lv1/img\/H7B14-38.png' \/><\/center> Tam gi\u00e1c $ABD$ vu\u00f4ng t\u1ea1i D n\u00ean theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $AD^{2}$$ = AB^{2} - BD^{2} \\\\ = 17^{2} - 15^{2} \\\\ = 289 - 225 \\\\ = 64 = 8^{2} $<br\/> $\\Rightarrow AD = 8 (cm) $ <br\/> $\\Rightarrow CD = AC - AD = 17 - 8 = 9 (cm) $ <br\/> Tam gi\u00e1c BCD vu\u00f4ng t\u1ea1i D n\u00ean theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $BC^{2}$$ = CD^{2} + BD^{2} \\\\ = 9^{2} + 15^{2} \\\\ = 81 + 225 \\\\ = 306 $<br\/> $\\Rightarrow BC = \\sqrt{306} (cm) $"}]}],"id_ques":1720}],"lesson":{"save":0,"level":1}}