{"segment":[{"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":" <b> Ph\u00e1t bi\u1ec3u sau ''\u0110\u00fang'' hay ''Sai''. <\/b> <br\/> <span class='basic_left'> ''N\u1ebfu hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' <\/span> ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-01.png' \/><\/center><span class='basic_pink'> Ph\u00e1t bi\u1ec3u tr\u00ean l\u00e0 sai. <\/span> <br\/> <b> V\u00ed d\u1ee5: <\/b> <br\/> Ta c\u00f3 $ AB = A'C' = 3(cm) AC = B'C' = 5(cm) $ <br\/> Nh\u01b0ng $\\triangle ABC \\neq \\triangle A'B'C' $ v\u00ec $BC \\neq B'C'$ <br\/> <span class='basic_left'> <i>Ph\u00e1t bi\u1ec3u tr\u00ean c\u00f3 th\u1ec3 s\u1eeda l\u1ea1i th\u00e0nh ph\u00e1t bi\u1ec3u \u0111\u00fang nh\u01b0 sau: <br\/> ''N\u1ebfu hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t <b> b\u1eb1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng <\/b> c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' <\/i> <\/span>","column":2}]}],"id_ques":1731},{"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>Ph\u00e1t bi\u1ec3u sau ''\u0110\u00fang'' hay ''Sai''.<\/b> <br\/> ''N\u1ebfu c\u1ea1nh huy\u1ec1n v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y b\u1eb1ng c\u1ea1nh huy\u1ec1n v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-02.png' \/><\/center> <span class='basic_pink'>Ph\u00e1t bi\u1ec3u tr\u00ean l\u00e0 \u0111\u00fang. <\/span> <br\/> V\u00ec khi \u0111\u00f3 hai tam gi\u00e1c s\u1ebd b\u1eb1ng nhau theo tr\u01b0\u1eddng h\u1ee3p g\u00f3c - c\u1ea1nh - g\u00f3c. ","column":2}]}],"id_ques":1732},{"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>Ph\u00e1t bi\u1ec3u sau ''\u0110\u00fang'' hay ''Sai''.<\/b> <br\/> ''N\u1ebfu hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y l\u1ea7n l\u01b0\u1ee3t b\u1eb1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-05.png' \/><\/center> <span class='basic_pink'>Ph\u00e1t bi\u1ec3u tr\u00ean l\u00e0 \u0111\u00fang. <\/span> <br\/> V\u00ec khi \u0111\u00f3 hai tam gi\u00e1c s\u1ebd b\u1eb1ng nhau theo tr\u01b0\u1eddng h\u1ee3p g\u00f3c - c\u1ea1nh - g\u00f3c. ","column":2}]}],"id_ques":1733},{"time":24,"part":[{"time":3,"title":"N\u1ed1i t\u1eeb ho\u1eb7c c\u1ee5m t\u1eeb \u1edf c\u1ed9t b\u00ean tr\u00e1i v\u1edbi c\u1ed9t b\u00ean ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c c\u00e2u ho\u00e0n ch\u1ec9nh","title_trans":"T\u00ecm c\u00e1c tam gi\u00e1c b\u1eb1ng nhau tr\u00ean h\u00ecnh v\u1ebd. ","audio":"","temp":"matching","correct":[["2","3","1"]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-06.png","left":["$\\triangle ADM = $","$\\triangle MDB = $","$\\triangle AMB = $"],"right":["$\\triangle AMC $ (c\u1ea1nh-c\u1ea1nh-c\u1ea1nh)","$\\triangle AEM $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn)","$\\triangle MEC $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) "],"top":100,"explain":" <span class='basic_left'> X\u00e9t tam gi\u00e1c vu\u00f4ng $ADM$ v\u00e0 tam gi\u00e1c vu\u00f4ng $AEM$ c\u00f3: <br\/>+ C\u1ea1nh huy\u1ec1n $AM$ chung <br\/>+ $\\widehat{DAM} = \\widehat{EAM} $ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\triangle ADM = \\triangle AEM $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow MD = ME$ <br\/> X\u00e9t tam gi\u00e1c vu\u00f4ng $MDB$ v\u00e0 tam gi\u00e1c vu\u00f4ng $MEC$ c\u00f3: <br\/> + $MB = MC$ (gi\u1ea3 thi\u1ebft) <br\/> + $MD = ME$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow \\triangle MDB = \\triangle MEC $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> Ta c\u00f2n suy ra: $AD = AE, BD = CE$ n\u00ean $AB = AC$ <br\/> $\\Rightarrow \\triangle AMB = \\triangle AMC $ (c.c.c)"}]}],"id_ques":1734},{"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 hai tam gi\u00e1c vu\u00f4ng $ABC$ v\u00e0 $DEF$ c\u00f3 $\\widehat{A} = \\widehat{D} = 90^{o}, AC = DF $ <br\/> H\u00e3y b\u1ed5 sung th\u00eam m\u1ed9t \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $\\triangle ABC = \\triangle DEF $ (c\u1ea1nh - g\u00f3c - c\u1ea1nh). ","select":["$AB = DE$"," $\\widehat{C} = \\widehat{F} $","$BC = EF $"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-07.png' \/><\/center> <span class='basic_left'> B\u1ed5 sung th\u00eam \u0111i\u1ec1u ki\u1ec7n $AB = DE$ th\u00ec $\\triangle ABC = \\triangle DEF $ (c\u1ea1nh - g\u00f3c - c\u1ea1nh). <br\/> V\u00ec khi \u0111\u00f3 c\u00f3: $+ \\,AB = DE \\\\ + \\,\\widehat{A} = \\widehat{D} = 90^{o} \\\\ +\\,AC = DF $ ","column":3}]}],"id_ques":1735},{"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 hai tam gi\u00e1c vu\u00f4ng $ABC$ v\u00e0 $DEF$ c\u00f3 $\\widehat{A} = \\widehat{D} = 90^{o}, AC = DF $ <br\/> H\u00e3y b\u1ed5 sung th\u00eam m\u1ed9t \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $\\triangle ABC = \\triangle DEF $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng). ","select":["$AB = DE$"," $\\widehat{C} = \\widehat{F} $","$BC = EF $"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-07.png' \/><\/center> <span class='basic_left'> B\u1ed5 sung th\u00eam \u0111i\u1ec1u ki\u1ec7n $BC = EF$ th\u00ec ta c\u00f3: <br\/> + $BC=EF$ <br\/> + $AC=DF$ <br\/> $\\Rightarrow \\triangle ABC = \\triangle DEF $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) ","column":3}]}],"id_ques":1736},{"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> Ph\u00e1t bi\u1ec3u sau ''\u0110\u00fang'' hay ''Sai''.<\/b> <br\/> <span class='basic_left'>''N\u1ebfu m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh \u1ea5y c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y b\u1eb1ng m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 m\u1ed9t g\u00f3c nh\u1ecdn \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh \u1ea5y c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' <\/span> ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-04.png' \/><\/center> <span class='basic_pink'> Ph\u00e1t bi\u1ec3u tr\u00ean l\u00e0 \u0111\u00fang <\/span> <br\/> Ta \u0111i ch\u1ee9ng minh n\u1ebfu $\\triangle ABC $ v\u00e0 $\\triangle A'B'C' $ c\u00f3: <br\/> $\\widehat{A} = \\widehat{A'}=90^o;\\widehat{B} = \\widehat{B'}$ v\u00e0 $AC=A'C'$ th\u00ec $\\triangle ABC = \\triangle A'B'C' $ <br\/> Th\u1eadt v\u1eady, do: $\\widehat{A} = \\widehat{A'}=90^o, \\widehat{B} = \\widehat{B'} \\\\ \\Rightarrow \\widehat{C} = \\widehat{C'} $<br\/> Khi \u0111\u00f3: <br\/> + $\\widehat{A} = \\widehat{A'}=90^o$ <br\/> + $AC=A'C'$ <br\/> + $\\widehat{C} = \\widehat{C'}$ <br\/> $\\Rightarrow \\triangle ABC = \\triangle A'B'C' $ (g.c.g).","column":2}]}],"id_ques":1737},{"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 $\\triangle DEF $ c\u00f3 $\\widehat{E} = \\widehat{F} $. V\u1ebd $DI \\perp EF (I \\in EF) $ <br\/> \u0110\u1ec3 ch\u1ee9ng minh $\\triangle DIE = \\triangle DIF $ b\u1ea1n B\u1eafc \u0111\u00e3 l\u00e0m nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-19.png' \/><\/center> <span class='basic_left'>X\u00e9t $\\triangle DIE $ c\u00f3: $\\widehat{D_{1}} + \\widehat{E} + \\widehat{DIE} = 180^{o} \\\\ \\Leftrightarrow \\widehat{D_{1}} + \\widehat{E} + 90^{o} = 180^{o} \\\\ \\Rightarrow \\widehat{D_{1}} = 180^{o} - (90^{o} + \\widehat{E}) $ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u0169ng c\u00f3: <br\/> $\\widehat{D_{2}}= 180^{o} - (90^{o} + \\widehat{F} ) $ <br\/> M\u00e0 $\\widehat{E} = \\widehat{F} $ (gi\u1ea3 thi\u1ebft) <br\/> $ \\Rightarrow \\widehat{D_{1}} = \\widehat{D_{2}} $ <br\/> X\u00e9t $\\triangle DIE $ v\u00e0 $\\triangle DIF $ c\u00f3: <br\/> + $\\widehat{D_{1}} =\\widehat{D_{2}} $ (ch\u1ee9ng minh tr\u00ean) <br\/> + c\u1ea1nh DI chung <br\/> + $ \\widehat{DIE} = \\widehat{DIF} (= 90^{o}) $ <br\/> Do \u0111\u00f3 $\\triangle DIE = \\triangle DIF$ (g.c.g) <\/span> <b> <u> H\u1ecfi: <\/u> <\/b> Ch\u1ee9ng minh c\u1ee7a b\u1ea1n B\u1eafc <b>\u0111\u00fang<\/b> hay <b>sai<\/b>? ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <span class='basic_pink'> B\u1ea1n B\u1eafc l\u00e0m nh\u01b0 tr\u00ean l\u00e0 \u0110\u00fang <\/span> ","column":2}]}],"id_ques":1738},{"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 $\\triangle DEF $ c\u00f3 $\\widehat{E} = \\widehat{F} $. V\u1ebd $DI \\perp EF (I \\in EF) $ <br\/> \u0110\u1ec3 ch\u1ee9ng minh $\\triangle DIE = \\triangle DIF $ b\u1ea1n Trung \u0111\u00e3 l\u00e0m nh\u01b0 sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-19.png' \/><\/center> <span class='basic_left'> Ta c\u00f3 $\\widehat{E} = \\widehat{F} $ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\triangle DEF $ c\u00e2n t\u1ea1i D <br\/> $\\Rightarrow DE = DF $ <br\/> X\u00e9t $\\triangle DIE (\\widehat{DIE} = 90^{o})<br\/>$ v\u00e0 $\\triangle DIF (\\widehat{DIF} = 90^{o} ) $ c\u00f3: <br\/> + $DE = DF$ (ch\u1ee9ng minh tr\u00ean) <br\/> + $\\widehat{E} = \\widehat{F} $ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\triangle DIE = \\triangle DIF $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn)<\/span> <b> <u> H\u1ecfi: <\/u> <\/b> Ch\u1ee9ng minh c\u1ee7a b\u1ea1n Trung <b>\u0111\u00fang<\/b> hay <b>sai<\/b>? ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'> <span class='basic_pink'> B\u1ea1n Trung l\u00e0m nh\u01b0 tr\u00ean l\u00e0 \u0110\u00fang <\/span> ","column":2}]}],"id_ques":1739},{"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'> <b>Ch\u1ecdn c\u00e2u tr\u1ea3 l\u1eddi sai <\/b> <br\/> Cho hai tam gi\u00e1c vu\u00f4ng $MNP$ v\u00e0 $DEF$ c\u00f3: $\\widehat{M} = \\widehat{D} = 90^{o}, MN = DE $ <br\/> Ta c\u00f3 $\\triangle MNP = \\triangle DEF $ khi: ","select":["A. $MP = DF$","B. $NP = EF$","C. $\\widehat{P} = \\widehat{E} $","D. $\\widehat{P} = \\widehat{F} $"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-20.png' \/><\/center> <span class='basic_left'> Ta d\u1ec5 d\u00e0ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c c\u00e1c tr\u01b0\u1eddng h\u1ee3p: <br\/> A. N\u1ebfu $MP = DF$ th\u00ec $\\triangle MNP = \\triangle DEF $ (c.g.c) <br\/> B. N\u1ebfu $NP = EF$ th\u00ec $\\triangle MNP = \\triangle DEF$ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> D. N\u1ebfu $\\widehat{P} = \\widehat{F} $ th\u00ec $\\triangle MNP = \\triangle DEF$ (g.c.g) <br\/><br\/> <span class='basic_pink'>C\u00e2u tr\u1ea3 l\u1eddi sai l\u00e0 C. <\/span> ","column":2}]}],"id_ques":1740},{"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":"S\u1ed1 c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau trong h\u00ecnh v\u1ebd sau l\u00e0: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-22.png' \/><\/center> ","select":["A. 1 ","B. 2","C. 3","D. 4"],"explain":" <span class='basic_left'> * $ \\triangle DIH = \\triangle DKH $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn). <br\/> V\u00ec: + C\u1ea1nh $DH$ chung <br\/> + $\\widehat{IDH} = \\widehat{KDH} $ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow IH = KH $ <br\/> * $\\triangle EIH = \\triangle FKH $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng). V\u00ec: <br\/> + $EH = FH$ (gi\u1ea3 thi\u1ebft) <br\/> + $IH = KH$ (ch\u1ee9ng minh tr\u00ean) <br\/> * $\\triangle DHE = \\triangle DHF $ (c\u1ea1nh - c\u1ea1nh - c\u1ea1nh). V\u00ec: <br\/> + c\u1ea1nh $DH$ chung <br\/> + $DE = DF$ (ch\u1ee9ng minh tr\u00ean) <br\/> + $HE = HF$ (gi\u1ea3 thi\u1ebft) <br\/> Nh\u01b0 v\u1eady c\u00f3 3 c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau trong h\u00ecnh v\u1ebd. <br\/><br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> ","column":4}]}],"id_ques":1741},{"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":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $\\widehat{B} = 30^{o} $. Khi \u0111\u00f3: ","select":["A. $AB = \\dfrac{1}{2}BC $ ","B. $AC = \\dfrac{1}{2}BC $","C. $AC > \\dfrac{1}{2}BC $","D. $AC < \\dfrac{1}{2}BC $"],"hint":"Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $AC$ l\u1ea5y \u0111i\u1ec3m $D$ sao cho $AD = AC$ ","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-24.png' \/><\/center> Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $AC$ l\u1ea5y \u0111i\u1ec3m $D$ sao cho $AD = AC$ <br\/> X\u00e9t $\\triangle BAD $ v\u00e0 $\\triangle BAC $ c\u00f3: <br\/> + $AD = AC$ <br\/> + $\\widehat{BAD} = \\widehat{BAC} (= 90^{o}) $ <br\/> + $AB$ l\u00e0 c\u1ea1nh chung. <br\/> $\\Rightarrow \\triangle ABD = \\triangle ABC (c.g.c)$ <br\/> $\\Rightarrow BD = BC $ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> Tam gi\u00e1c $BDC$ c\u00e2n c\u00f3 $\\widehat{C} = 60^{o} $ n\u00ean l\u00e0 tam gi\u00e1c \u0111\u1ec1u. <br\/> Do \u0111\u00f3 $BC = DC = 2AC$ <br\/> Hay $AC = \\dfrac{1}{2}BC $<br\/><br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span> ","column":2}]}],"id_ques":1742},{"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'>X\u00e9t t\u00ednh ch\u1ea5t: '' N\u1ebfu c\u1ea1nh huy\u1ec1n v\u00e0 m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng n\u00e0y b\u1eb1ng c\u1ea1nh huy\u1ec1n v\u00e0 m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ee7a tam gi\u00e1c vu\u00f4ng kia th\u00ec hai tam gi\u00e1c vu\u00f4ng \u0111\u00f3 b\u1eb1ng nhau.'' <\/span> <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh t\u00ednh ch\u1ea5t tr\u00ean: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-26.png' \/><\/center> <br\/> <span class='basic_left'>(1) T\u1eeb \u0111\u00f3 suy ra $\\triangle ABC = \\triangle DEF $ (c.c.c)<br\/> (2) X\u00e9t $\\triangle DEF $ vu\u00f4ng t\u1ea1i D, theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $DE^{2} + DF^{2} = EF^{2}$ n\u00ean: <br\/> $DE^{2} = EF^{2} - DF^{2} = a^{2} - b^{2} $ <br\/> (3) \u0110\u1eb7t $BC = EF = a, AC = DF = b$ <br\/> (4) X\u00e9t $\\triangle ABC $ vu\u00f4ng t\u1ea1i A, theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $AB^{2} + AC^{2} = BC^{2}$ n\u00ean: <br\/> $AB^{2} = BC^{2} - AC^{2} = a^{2} - b^{2} $ <br\/> (5) Do \u0111\u00f3: $AB^{2} = DE^{2} (= a^{2} - b^{2}) $ <br\/> N\u00ean $AB = DE$ <\/span> ","select":["A. (3), (4), (2), (5) v\u00e0 (1) ","B. (1), (2), (3), (4) v\u00e0 (5) ","C. (1), (3), (5), (2) v\u00e0 (4) ","D. (1), (5), (2), (4) v\u00e0 (3) "],"hint":"Ch\u1ee9ng minh hai tam gi\u00e1c b\u1eb1ng nhau theo tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh-c\u1ea1nh-c\u1ea1nh. ","explain":"<span class='basic_left'> \u0110\u1eb7t $BC = EF = a, AC = DF = b$ <br\/> X\u00e9t $\\triangle ABC $ vu\u00f4ng t\u1ea1i A, theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $AB^{2} + AC^{2} = BC^{2}$ n\u00ean: <br\/> $AB^{2} = BC^{2} - AC^{2} = a^{2} - b^{2} $ <br\/> X\u00e9t $\\triangle DEF $ vu\u00f4ng t\u1ea1i D, theo \u0111\u1ecbnh l\u00ed Py-ta-go ta c\u00f3: <br\/> $DE^{2} + DF^{2} = EF^{2}$ n\u00ean: <br\/> $DE^{2} = EF^{2} - DF^{2} = a^{2} - b^{2} $ <br\/> Do \u0111\u00f3: $AB^{2} = DE^{2} (= a^{2} - b^{2}) $ <br\/> N\u00ean $AB = DE$ <br\/> T\u1eeb \u0111\u00f3 suy ra $\\triangle ABC = \\triangle DEF $ (c.c.c) <br\/><br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span> ","column":2}]}],"id_ques":1743},{"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":"Cho $\\triangle ABC $ v\u00e0 $\\triangle MNP $ c\u00f3 $\\widehat{A} = \\widehat{M} = 90^{o}, \\widehat{C} = \\widehat{P}. $ <br\/> C\u1ea7n th\u00eam \u0111i\u1ec1u ki\u1ec7n g\u00ec \u0111\u1ec3 $\\triangle ABC = \\triangle MNP$ theo tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh g\u00f3c vu\u00f4ng - g\u00f3c nh\u1ecdn k\u1ec1. ","select":["A. $AC = MP$ ","B. $AB = MN$ ","C. $BC = NP$ ","D. $AC = NP$ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-28.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle ABC $ v\u00e0 $\\triangle MNP $ c\u00f3: <br\/> + $\\widehat{A} = \\widehat{M} = 90^{o}$ <br\/>+ $AC = MP$ <br\/> + $ \\widehat{C} = \\widehat{P} $ <br\/> $\\Rightarrow \\triangle ABC = \\triangle MNP $ (c\u1ea1nh g\u00f3c vu\u00f4ng - g\u00f3c nh\u1ecdn k\u1ec1) <br\/><br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span> ","column":2}]}],"id_ques":1744},{"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":"Cho $\\triangle ABC $ v\u00e0 $\\triangle MNP $ c\u00f3 $\\widehat{B} = \\widehat{N} = 90^{o}, AC = MP, \\widehat{A} = \\widehat{P}. $ Khi \u0111\u00f3: ","select":["A. $\\triangle ABC = \\triangle PNM $","B. $\\triangle ACB = \\triangle PNM $ ","C. $\\triangle BAC = \\triangle MNP $ ","D. $\\triangle ABC = \\triangle PMN $ "],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-29.png' \/><\/center> <span class='basic_left'> X\u00e9t $\\triangle ABC $ v\u00e0 $\\triangle MNP $ c\u00f3: <br\/>+ $\\widehat{B} = \\widehat{N} = 90^{o}$ + $ AC = MP$ <br\/> + $\\widehat{A} = \\widehat{P} $ <br\/> $\\Rightarrow \\triangle ABC = \\triangle PNM $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) <br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span> ","column":2}]}],"id_ques":1745},{"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 $ABC$ c\u00e2n t\u1ea1i $A$. K\u1ebb $AD$ vu\u00f4ng g\u00f3c v\u1edbi $BC$. <br\/> Khi \u0111\u00f3 $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $A$ <b> \u0111\u00fang <\/b> hay <b> sai<\/b> ","select":["\u0110\u00fang","Sai"],"explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-39.png' \/><\/center> Hai tam gi\u00e1c vu\u00f4ng $ADB$ v\u00e0 $ADC$ c\u00f3: <br\/> + c\u1ea1nh $AD$ chung <br\/> + $AB = AC$ <br\/> $\\Rightarrow \\triangle ADB = \\triangle ADC $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> Suy ra $\\widehat{BAD} = \\widehat{CAD} $ (c\u1eb7p g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> Do \u0111\u00f3 $AD$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $A$. ","column":2}]}],"id_ques":1746},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho tam gi\u00e1c ABC c\u00e2n t\u1ea1i A. K\u1ebb $BD \\perp AC, CE \\perp AB $. <br\/> G\u1ecdi K l\u00e0 giao \u0111i\u1ec3m c\u1ee7a BD v\u00e0 CE. <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh AK l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c A. ","temp":"sequence","correct":[[[3],[1],[2],[4],[5]]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-40.png","left":["Ta c\u00f3: $\\triangle ADK = \\triangle AEK $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng)","Ta c\u00f3: $\\triangle ADB = \\triangle AEC $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn)","$\\Rightarrow AD = AE $","$\\Rightarrow \\widehat{A_{1}} = \\widehat{A_{2}} $ ","V\u1eady $AK$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c A. "],"top":55,"explain":" <span class='basic_left'> Ta x\u00e9t hai tam gi\u00e1c vu\u00f4ng $ADB$ v\u00e0 $AEC$ c\u00f3: <br\/> + $\\widehat{A}$ chung <br\/> + $AB=AC$ <br\/> $\\Rightarrow \\triangle ADB = \\triangle AEC $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow AD = AE $ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/>Ta x\u00e9t hai tam gi\u00e1c vu\u00f4ng $ADK$ v\u00e0 $AEK$ c\u00f3: <br\/> + $AE=AD$ (ch\u1ee9ng minh tr\u00ean) <br\/> + $AK$ l\u00e0 c\u1ea1nh chung <br\/> $\\Rightarrow \\triangle ADK = \\triangle AEK $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/>$\\Rightarrow \\widehat{A_{1}} = \\widehat{A_{2}} $ <br\/> V\u1eady $AK$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $A$. "}]}],"id_ques":1747},{"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","t","f"]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-41.png' \/><\/center> <br\/> Cho $\\triangle ABC$ c\u00f3 $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BC, AM$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $A$. <br\/> K\u1ebb $MH \\perp AB, MK \\perp AC $. Khi \u0111\u00f3: ","image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["$\\triangle AMH = \\triangle AMK $","$MH = MK$","$\\triangle MHB = \\triangle MKC $","$\\triangle ABC $ c\u00e2n t\u1ea1i B "],"explain":[" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-41.png' \/><\/center> <span class='basic_left'> 1 - \u0110\u00fang, do: <br\/> + $AM$ l\u00e0 c\u1ea1nh chung <br\/> + $\\widehat{HAM}=\\widehat{KAM}$ (AM l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAC}$) <br\/> $\\Rightarrow \\triangle AMH = \\triangle AMK $ (c\u1ea1nh huy\u1ec1n - g\u00f3c nh\u1ecdn )<\/span>","<span class='basic_left'> 2 - \u0110\u00fang, do $\\triangle AMH = \\triangle AMK $ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow MH = MK$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng)<\/span>","<span class='basic_left'> 3 - \u0110\u00fang, do: <br\/> + $BM=MC$ (gi\u1ea3 thi\u1ebft) <br\/> + $MH=MK$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow\\triangle MHB = \\triangle MKC $ (c\u1ea1nh huy\u1ec1n - c\u1ea1nh g\u00f3c vu\u00f4ng) <\/span> ","<span class='basic_left'> 4 - Sai. V\u00ec $\\widehat{B} = \\widehat{C} \\Rightarrow ABC $ c\u00e2n t\u1ea1i A. <\/span> "]}]}],"id_ques":1748},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["15"]]],"list":[{"point":5,"width":20,"content":"","type_input":"","ques":" <span class='basic_left'> Cho $\\triangle ABC = \\triangle DEF, \\triangle DEF = \\triangle GHI $. <br\/> T\u00ednh chu vi tam gi\u00e1c $ABC$ bi\u1ebft $AB = 4cm, DF = 6cm, HI = 5cm.$ <br\/> <b>\u0110\u00e1p \u00e1n:<\/b> $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}(cm)$ ","explain":" <span class='basic_left'> Theo gi\u1ea3 thi\u1ebft: $\\triangle ABC = \\triangle DEF, \\triangle DEF = \\triangle GHI$ n\u00ean: <br\/> $AB = 4cm \\\\ AC = DF = GI = 6cm \\\\ BC = EF = HI = 5cm $ <br\/> Chu vi tam gi\u00e1c $ABC$ l\u00e0: <br\/> $ 4 + 6 + 5 = 15cm $ "}]}],"id_ques":1749},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["55"]]],"list":[{"point":5,"width":20,"content":"","type_input":"","ques":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd, bi\u1ebft: $BA = BD, \\widehat{ABC} = \\widehat{DBC}, \\widehat{ACB} = 55^{o} $ <br\/> S\u1ed1 \u0111o g\u00f3c $\\widehat{DCB} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o}$ <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai15/lv1/img\/H7B15-42.png' \/><\/center>","explain":" <span class='basic_left'> X\u00e9t $\\triangle ABC $ v\u00e0 $\\triangle DBC $ c\u00f3: <br\/> + $AB = DB$ (gi\u1ea3 thi\u1ebft) <br\/>+ $\\widehat{ABC} = \\widehat{DBC}$ (gi\u1ea3 thi\u1ebft) <br\/> + C\u1ea1nh $BC$ chung <br\/> $\\Rightarrow \\triangle ABC = \\triangle DBC (c.g.c) $ <br\/> $\\Rightarrow \\widehat{ACB} = \\widehat{DCB} $ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> M\u00e0 $\\widehat{ACB} = 55^{o} \\Rightarrow \\widehat{DCB} = 55^{o} $ "}]}],"id_ques":1750}],"lesson":{"save":0,"level":1}}