{"segment":[{"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 \u0111\u01b0\u1eddng th\u1eb3ng a c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng b, c. Sao cho trong c\u00e1c g\u00f3c t\u1ea1o th\u00e0nh t\u1eeb a, b, c c\u00f3 m\u1ed9t c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau v\u1edbi s\u1ed1 \u0111o b\u1eb1ng $35^{o}$ nh\u01b0 h\u00ecnh v\u1ebd. H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t. <\/span> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-45.png' \/><\/center> ","select":["A. $\\widehat{A_{4}} = 35^{o}$ ","B. $\\widehat{A_{3}} = 145^{o}$ ","C. $\\widehat{B_{2}} = 35^{o}$ ","D. T\u1ea5t c\u1ea3 c\u00e1c \u0111\u00e1p \u00e1n tr\u00ean \u0111\u1ec1u \u0111\u00fang "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>+ $\\widehat{A_{2}} = \\widehat{A_{4}}$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh)<br\/>M\u00e0 $\\widehat{A_{2}} = 35^{o}$ (gt)<br\/>$\\Rightarrow$ $\\widehat{A_{4}} = 35^{o}$<br\/>+ $\\widehat{A_{2}} + \\widehat{A_{3}} = 180^{o}$ (hai g\u00f3c k\u1ec1 b\u00f9)<br\/>$\\Rightarrow$ $\\widehat{A_{3}} = 180^{o} - \\widehat{A_{2}} = 180^{o} - 35^{o} = 145^{o}$<br\/>+ $\\widehat{B_{4}} = \\widehat{B_{2}}$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh)<br\/>L\u1ea1i c\u00f3: $\\widehat{B_{4}} = 35^{o}$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\widehat{B_{2}} = 35^{o}$<br\/>V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'> D. T\u1ea5t c\u1ea3 c\u00e1c \u0111\u00e1p \u00e1n tr\u00ean \u0111\u1ec1u \u0111\u00fang<\/span><\/span> <br\/><\/span>","column":2}]}],"id_ques":1511},{"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 h\u00ecnh v\u1ebd, bi\u1ebft AB \/\/ MD; BC \/\/ EM. Khi \u0111\u00f3: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-32.png' \/> <\/center> ","select":["A. $\\widehat{AEM} = \\widehat{MDC}$ ","B. $\\widehat{BAM} = \\widehat{AMD}$","C. $\\widehat{ABC} < \\widehat{DME}$ "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> AB \/\/ MD (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ + $\\widehat{ABC} = \\widehat{MDC}$ (c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb) (1)<br\/> + $ \\widehat{BAM} + \\widehat{AMD} = 180^{o}$ ( c\u1eb7p g\u00f3c trong c\u00f9ng ph\u00eda) <span class='basic_pink'> $\\Rightarrow$ \u0111\u00e1p \u00e1n B sai<\/span><br\/> + $\\widehat{ABC} + \\widehat{BDM} = 180^{o}$ ( c\u1eb7p g\u00f3c trong c\u00f9ng ph\u00eda) (2) <br\/>BC \/\/ EM (gt) <br\/>$\\Rightarrow$ + $\\widehat{ABC} = \\widehat{AEM}$ (c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb) (3)<br\/> + $\\widehat{EMD} + \\widehat{BDM} = 180^{o}$ ( c\u1eb7p g\u00f3c trong c\u00f9ng ph\u00eda) (4)<br\/>T\u1eeb (1) v\u00e0 (3) $\\Rightarrow$ $\\widehat{AEM} = \\widehat{MDC}$ <span class='basic_pink'>(\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/span><br\/>T\u1eeb (2) v\u00e0 (4) $\\Rightarrow$ $\\widehat{ABC} = \\widehat{EMD}$ <span class='basic_pink'>(\u0111\u00e1p \u00e1n C sai)<\/span><br\/>V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>A. $\\widehat{AEM} = \\widehat{MDC}$<\/span><\/span> <br\/><\/span>","column":3}]}],"id_ques":1512},{"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":"Ch\u1ecdn c\u00e2u tr\u1ea3 l\u1eddi sai. <br\/> Tr\u00ean h\u00ecnh v\u1ebd, bi\u1ebft Dx l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{mDn} $ <br\/> Ta c\u00f3 Dx \/\/ HK khi: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-31.png' \/> <\/center> ","select":["A. $\\widehat{mDx} = \\widehat{DKH}$ ","B. $\\widehat{xDK} = \\widehat{DKH}$","C. $\\widehat{xDK} = \\widehat{nKH}$ ","D. $\\widehat{mDx} = \\widehat{DHK}$ "],"hint":"","explain":" <span class='basic_left'>Ta c\u00f3: Dx l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{mDn}$ ( gi\u1ea3 thi\u1ebft) <br\/>$\\Rightarrow$ $\\widehat{mDx} = \\widehat{xDK}$ (1)<br\/>L\u1ea1i c\u00f3: Dx \/\/ HK (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $\\widehat{xDK} = \\widehat{DKH}$ (c\u1eb7p g\u00f3c so le trong) (2) <span class='basic_pink'>(\u0111\u00e1p \u00e1n B \u0111\u00fang)<\/span><br\/> $\\widehat{mDx} = \\widehat{DHK}$ (c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb) <span class='basic_pink'>(\u0111\u00e1p \u00e1n D \u0111\u00fang)<\/span><br\/>T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $\\widehat{mDx} = \\widehat{DKH}$ <span class='basic_pink'>(\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/span><br\/>\u0110\u00e1p \u00e1n C sai v\u00ec: $\\widehat{xDK} + \\widehat{nKH} = 180^{o}$<br\/>V\u1eady \u0111\u00e1p \u00e1n sai l\u00e0: <span class='basic_pink'>C<\/span><\/span>","column":2}]}],"id_ques":1513},{"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":"Cho \u0111\u01b0\u1eddng th\u1eb3ng AB c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng a, b sao cho trong c\u00e1c g\u00f3c t\u1ea1o th\u00e0nh t\u1eeb AB, a, b c\u00f3 m\u1ed9t c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau v\u1edbi s\u1ed1 \u0111o b\u1eb1ng $30^{o} $ nh\u01b0 h\u00ecnh v\u1ebd. C\u00e2u n\u00e0o sau \u0111\u00e2y \u0111\u00fang? <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-30.png' \/> <\/center> ","select":["A. Ch\u1ec9 c\u00f3 m\u1ed9t c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau. ","B. C\u00f3 hai c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau ","C. C\u00f3 b\u1ed1n c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau ","D. C\u1ea3 ba ph\u00e1t bi\u1ec3u tr\u00ean \u0111\u1ec1u sai. "],"hint":"","explain":" Ta c\u00f3 $\\widehat{A_{2}} = \\widehat{B_{4}} (= 30^{o}) $ <br\/> M\u00e0 hai g\u00f3c n\u00e0y \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb n\u00ean a \/\/ b <br\/> V\u00ec a \/\/ b n\u00ean c\u00f3 2 c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau, 4 c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau. <br\/><br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> ","column":2}]}],"id_ques":1514},{"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":"Cho c l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi hai \u0111\u01b0\u1eddng th\u1eb3ng song song a, b. Bi\u1ebft m l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0o \u0111\u00f3. Ph\u00e1t bi\u1ec3u n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang? ","select":["A. N\u1ebfu m vu\u00f4ng g\u00f3c v\u1edbi c th\u00ec m song song v\u1edbi a v\u00e0 b. ","B. N\u1ebfu m song song v\u1edbi c th\u00ec m vu\u00f4ng g\u00f3c v\u1edbi a v\u00e0 b. ","C. N\u1ebfu m vu\u00f4ng g\u00f3c v\u1edbi a th\u00ec m song song v\u1edbi c. ","D. C\u1ea3 ba ph\u00e1t bi\u1ec3u tr\u00ean \u0111\u1ec1u \u0111\u00fang. "],"hint":"V\u1ebd h\u00ecnh r\u1ed3i t\u00ecm ra \u0111\u00e1p \u00e1n.","explain":" C\u1ea3 ba ph\u00e1t bi\u1ec3u tr\u00ean \u0111\u1ec1u \u0111\u00fang. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-28A.png' \/><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-28B.png' \/><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-28C.png' \/><\/center> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span> ","column":1}]}],"id_ques":1515},{"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":"","select":["A. G\u00f3c $\\widehat{MON} $ v\u00e0 g\u00f3c $\\widehat{POQ} $ c\u00f3 OM l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia OP v\u00e0 ON l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia OQ n\u00ean ch\u00fang l\u00e0 hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh. ","B. Hai g\u00f3c $\\widehat{MON} $ v\u00e0 $\\widehat{POQ} $ \u0111\u1ed1i \u0111\u1ec9nh n\u00ean $\\widehat{MON} = \\widehat{POQ} $","C. Hai g\u00f3c $\\widehat{MON} $ v\u00e0 $\\widehat{POQ} $ b\u1eb1ng nhau n\u00ean ch\u00fang l\u00e0 hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh. ","D. C\u00e2u A v\u00e0 B \u0111\u00fang"],"hint":"","explain":" \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <br\/> C\u00e2u C. Sai. V\u00ec hai g\u00f3c b\u1eb1ng nhau ch\u01b0a ch\u1eafc \u0111\u00e3 \u0111\u1ed1i \u0111\u1ec9nh. V\u00ed d\u1ee5: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-26.png' \/><\/center> <br\/> <br\/> <span class='basic_pink'> <\/span> ","column":1}]}],"id_ques":1516},{"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":[[["45"],["135"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" Cho h\u00ecnh v\u1ebd, bi\u1ebft $a \\perp c, b \\perp c, \\widehat{B_{3}} = 45^{o} $ <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-24.png' \/><\/center> T\u00ednh: $ \\widehat{A_{1}} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} \\\\ \\widehat{A_{4}} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" Ta c\u00f3 $a \\perp c, b \\perp c $ n\u00ean a \/\/ b <br\/> V\u00ec a \/\/ b n\u00ean $\\widehat{A_{1}} = \\widehat{B_{3}} = 45^{o} $ (c\u1eb7p g\u00f3c so le trong) <br\/> L\u1ea1i c\u00f3: $\\widehat{A_{1}} + \\widehat{A_{4}} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> $\\Rightarrow \\widehat{A_{4}} = 180^{o} - 45^{o} = 135^{o} $<\/span> <br\/> <br\/> <span class='basic_pink'> V\u1eady: $ \\widehat{A_{1}} = 45^{o} \\\\ \\widehat{A_{4}} = 135^{o}$ <\/span><\/span> <br\/>"}]}],"id_ques":1517},{"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":[[["108"],["72"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" T\u00ecm x v\u00e0 y trong h\u00ecnh v\u1ebd, bi\u1ebft 2x = 3y . <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-22.png' \/><\/center> <br\/> \u0110\u00e1p \u00e1n: $ x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} \\\\ y = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'>Ta c\u00f3 $ a \\perp n, b \\perp n$ n\u00ean a \/\/ b <br\/> V\u00ec a \/\/ b n\u00ean $x + y = 180^{o} $ <br\/>Theo b\u00e0i c\u00f3: $2x = 3y \\Leftrightarrow \\dfrac{x}{3} = \\dfrac{y}{2} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta \u0111\u01b0\u1ee3c: <br\/> $ \\dfrac{x}{3} = \\dfrac{y}{2} = \\dfrac{x+y}{2+3} = \\dfrac{180^{o}}{5} = 36^{o} \\\\ \\Rightarrow x = 3.36^{o} = 108^{o} \\\\ y = 2.36 = 72^{o} $ <\/span> <br\/> <br\/> <span class='basic_pink'> V\u1eady: $ x = 108^{o} \\\\ y = 72^{o} $ <\/span><\/span> <br\/>"}]}],"id_ques":1518},{"time":24,"part":[{"time":3,"title":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u","title_trans":"Cho h\u00ecnh v\u1ebd <br\/> H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd ch\u1ee9ng minh AB \/\/ CD ","temp":"sequence","correct":[[[4],[2],[1],[3]]],"list":[{"point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-20.png","left":["M\u00e0 $\\widehat{APQ}$ v\u00e0 $\\widehat{CQF}$ \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb. V\u1eady AB \/\/ CD","m\u00e0 $\\widehat{EPB} = \\widehat{CQF} $ (gi\u1ea3 thi\u1ebft)","Ta c\u00f3 $\\widehat{EPB} = \\widehat{APQ} $ (\u0111\u1ed1i \u0111\u1ec9nh)","Suy ra $\\widehat{APQ} = \\widehat{CQF}$"],"top":55,"hint":"","explain":"Ta c\u00f3 $\\widehat{EPB} = \\widehat{APQ} $ (\u0111\u1ed1i \u0111\u1ec9nh) <br\/> m\u00e0 $\\widehat{EPB} = \\widehat{CQF} $ (gi\u1ea3 thi\u1ebft) <br\/> Suy ra $\\widehat{APQ} = \\widehat{CQF} (= \\widehat{EPB})$ <br\/> Hai g\u00f3c n\u00e0y \u1edf v\u1ecb tr\u00ed \u0111\u1ed3ng v\u1ecb n\u00ean AB \/\/ CD. "}]}],"id_ques":1519},{"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":[[["36"],["144"],["36"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho hai \u0111\u01b0\u1eddng th\u1eb3ng x'x v\u00e0 y'y. G\u1ecdi A v\u00e0 B l\u00e0 hai \u0111i\u1ec3m l\u1ea7n l\u01b0\u1ee3t tr\u00ean x'x v\u00e0 y'y sao cho hai tia Ax, By c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng AB. Bi\u1ebft $ \\widehat{A_{1}} + \\widehat{A_{2}} + \\widehat{B_{1}} = 216^{o} $ v\u00e0 $\\widehat{A_{2}} = 4\\widehat{A_{1}} $ <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-18.png' \/><\/center> T\u00ednh: $ \\widehat{A_{1}} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} \\\\ \\widehat{A_{2}} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} \\\\ \\widehat{B_{1}} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'> Ta c\u00f3 $\\widehat{A_{1}} + \\widehat{A_{2}} = 180^{o} $ (hai g\u00f3c k\u1ec1 b\u00f9) m\u00e0 $\\widehat{A_{2}} = 4\\widehat{A_{1}}$ <br\/> do \u0111\u00f3 $\\widehat{A_{1}} + 4\\widehat{A_{1}} = 180^{o} $ hay $5\\widehat{A_{1}} = 180^{o}$ <br\/> suy ra $\\widehat{A_{1}} = 36^{o}$, t\u1eeb \u0111\u00f3 $\\widehat{A_{2}} = 180^{o} - 36^{o} = 144^{o}$ <br\/> Theo gi\u1ea3 thi\u1ebft th\u00ec $ \\widehat{A_{1}} + \\widehat{A_{2}} + \\widehat{B_{1}} = 216^{o} $ <br\/> suy ra $ \\widehat{B_{1}} = 216^{o} - ( \\widehat{A_{1}} + \\widehat{A_{2}}) = 216^{o} - 180^{o} = 36^{o} $<\/span> <br\/> <br\/> <span class='basic_pink'> V\u1eady: $ \\widehat{A_{1}} = 36^{o} \\\\ \\widehat{A_{2}} = 144^{o} \\\\ \\widehat{B_{1}} = 36^{o} $ <\/span><\/span> <br\/>"}]}],"id_ques":1520},{"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":[[["210"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho h\u00ecnh v\u1ebd <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-15.png' \/><\/center> <br\/> T\u1ed5ng s\u1ed1 \u0111o g\u00f3c $\\widehat{A_{1}} + \\widehat{B_{1}} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'>Ta c\u00f3: $a \\perp d, b \\perp d $ n\u00ean a \/\/ b (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/> V\u00ec a \/\/ b n\u00ean $\\widehat{A_{2}} + \\widehat{B_{2}} = 180^{o} $ (hai g\u00f3c trong c\u00f9ng ph\u00eda) <br\/> $\\Rightarrow \\widehat{A_{2}} = 180^{o} - \\widehat{B_{2}} = 180^{o} - 75^{o} = 105^{o} $ <br\/> M\u1eb7t kh\u00e1c, c\u00f3 $\\widehat{A_{1}} = \\widehat{A_{2}} (= 105^{o} ) $ (hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh) <br\/> a \/\/ b n\u00ean $\\widehat{B_{1}} = \\widehat{A_{2}} (= 105^{o} ) $ (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) <br\/> V\u1eady $\\widehat{A_{1}} + \\widehat{B_{1}} = 105^{o} + 105^{o} = 210^{o} $<\/span> <br\/> <br\/> <span class='basic_pink'>\u0110\u00e1p s\u1ed1 l\u00e0: $210^{o}$ <\/span><\/span> <br\/>"}]}],"id_ques":1521},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","f","t"]],"list":[{"point":5,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng th\u00ec \u0111i qua trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3","Hai g\u00f3c c\u00f3 chung \u0111\u1ec9nh l\u00e0 hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh","Hai g\u00f3c b\u1eb1ng nhau l\u00e0 hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh","\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng th\u00ec vu\u00f4ng g\u00f3c v\u1edbi \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3."],"hint":"","explain":["\u0110\u00fang","<br\/>Sai. V\u00ed d\u1ee5, <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-12.png' \/><\/center> ","<br\/>Sai. V\u00ed d\u1ee5, <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-12.png' \/><\/center>","<br\/> \u0110\u00fang "]}]}],"id_ques":1522},{"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":"Cho ba \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t a, b, c. <br\/> Bi\u1ebft $ a \\perp c$ v\u00e0 $b \\perp c, $ ta suy ra: ","select":["A. a v\u00e0 b c\u1eaft nhau","B. a v\u00e0 b tr\u00f9ng nhau ","C. a v\u00e0 b song song v\u1edbi nhau ","D. a v\u00e0 b vu\u00f4ng g\u00f3c v\u1edbi nhau"],"hint":"V\u1ebd h\u00ecnh \u0111\u1ec3 t\u00ecm ra \u0111\u00e1p \u00e1n","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-10.png' \/><\/center> Ba \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t a, b, c. <br\/> C\u00f3 $ a \\perp c, b \\perp c $ th\u00ec khi \u0111\u00f3 a \/\/ b <br\/> <br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span> ","column":2}]}],"id_ques":1523},{"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":[[["100"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho h\u00ecnh v\u1ebd, c\u00f3 $\\widehat{B_{1}} = 45^{o}, \\widehat{D_{1}} = 55^{o} $ v\u00e0 AB \/\/ CD . <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-09A.png' \/><\/center> <br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\widehat{xOy} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-09B.png' \/><\/center> <br\/> K\u1ebb tia Ot \/\/ AB <br\/> $Ot \/\/ AB \\\\ AB \/\/ CD $ <br\/> n\u00ean Ot \/\/ CD (c\u00f9ng song song v\u1edbi AB) <br\/> $ AB \/\/ Ot \\Rightarrow \\widehat{O_{1}} = \\widehat{B_{1}} = 45^{o} $ (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) <br\/> $ Ot \/\/ CD \\Rightarrow \\widehat{O_{2}} = \\widehat{D_{1}} = 55^{o} $ (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) <br\/> Suy ra $\\widehat{xOy} = \\widehat{O_{1}} + \\widehat{O_{2}} = 45^{o} + 55^{o} = 100^{o} $ <br\/> <br\/> <span class='basic_pink'>V\u1eady $ \\widehat{xOy} = 100^{o} $ <\/span><\/span> <br\/>"}]}],"id_ques":1524},{"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":[[["50"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" Cho g\u00f3c AOB c\u00f3 s\u1ed1 \u0111o b\u1eb1ng $130^{o} $. V\u1ebd ra ngo\u00e0i g\u00f3c \u0111\u00f3 c\u00e1c tia OM v\u00e0 ON sao cho $OM \\perp OA, ON \\perp OB $ <br\/> S\u1ed1 \u0111o g\u00f3c $\\widehat{MON} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-08.png' \/><\/center> Ta c\u00f3 $OM \\perp OA $ n\u00ean $\\widehat{MOA} = 90^{o} $ <br\/> $ON \\perp OB $ n\u00ean $\\widehat{BON} = 90^{o} $ <br\/> Do \u0111\u00f3, $\\widehat{MON} $$ = 360^{o} - (\\widehat{AOB} + \\widehat{AOM} + \\widehat{BON}) \\\\ = 360^{o} - (130^{o} + 90^{o} + 90^{o}) \\\\ = 360^{o} - 310^{o} \\\\ = 50^{o} $<br\/> <br\/> <span class='basic_pink'>V\u1eady $ \\widehat{MON} = 50^{o} $ <\/span><\/span> <br\/>"}]}],"id_ques":1525},{"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":"Cho h\u00ecnh v\u1ebd, bi\u1ebft a \/\/ b, $ c \\perp a$ <br\/> C\u00e2u n\u00e0o sau \u0111\u00e2y l\u00e0 sai: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-05.png' \/><\/center>","select":["A. $c \\perp b $ ","B. $\\widehat{ADC} + \\widehat{BCD} = 180^{o} $ ","C. $\\widehat{D_{1}} = \\widehat{B_{4}} $ ","D. $\\widehat{D_{2}} = \\widehat{B_{3}} $ "],"hint":"","explain":" <span class='basic_left'>Ta c\u00f3: a \/\/ b (gi\u1ea3 thi\u1ebft)<br\/>$ c \\perp a$ (gi\u1ea3 thi\u1ebft)<br\/>$\\Rightarrow$ $ c \\perp a$ (t\u00ednh ch\u1ea5t quan h\u1ec7 gi\u1eefa t\u00ednh vu\u00f4ng g\u00f3c v\u1edbi t\u00ednh song song) <span class='basic_pink'>(\u0111\u00e1p \u00e1n A \u0111\u00fang)<\/span><br\/>a \/\/ b (gi\u1ea3 thi\u1ebft)<br\/> Suy ra:<br\/>$\\widehat{ADC} + \\widehat{BCD} = 180^{o} $ (hai g\u00f3c trong c\u00f9ng ph\u00eda) <span class='basic_pink'>(\u0111\u00e1p \u00e1n B \u0111\u00fang)<\/span><br\/>$\\widehat{D_{1}} = \\widehat{B_{4}} $ (c\u1eb7p g\u00f3c so le trong) <span class='basic_pink'>(\u0111\u00e1p \u00e1n C \u0111\u00fang)<\/span><br\/> V\u00ec AB kh\u00f4ng song song v\u1edbi DC n\u00ean $\\widehat{D_{2}} $ v\u00e0 $ \\widehat{B_{3}} $ l\u00e0 hai g\u00f3c so le trong kh\u00f4ng b\u1eb1ng nhau. <br\/> <br\/> <span class='basic_pink'>Ch\u1ecdn \u0111\u00e1p \u00e1n D. <\/span><\/span> ","column":2}]}],"id_ques":1526},{"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":[[["190"],["90"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Qua \u0111i\u1ec3m O tr\u00ean m\u1eb7t ph\u1eb3ng v\u1ebd 10 \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t. <br\/> S\u1ed1 g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} (g\u00f3c)$ <br\/> S\u1ed1 c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh kh\u00e1c g\u00f3c b\u1eb9t l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} $","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>Hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh l\u00e0 hai g\u00f3c m\u00e0 m\u1ed7i c\u1ea1nh c\u1ee7a g\u00f3c n\u00e0y l\u00e0 tia \u0111\u1ed1i m\u1ed9t c\u1ea1nh c\u1ee7a g\u00f3c kia. <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <span class='basic_left'> 10 \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t qua \u0111i\u1ec3m O t\u1ea1o th\u00e0nh 20 tia, trong \u0111\u00f3 m\u1ed7i tia t\u1ea1o v\u1edbi 19 tia c\u00f2n l\u1ea1i 19 g\u00f3c, <br\/> v\u1eady $20$ tia t\u1ea1o th\u00e0nh: $20.19 = 380 $(g\u00f3c) <br\/> Tuy nhi\u00ean m\u1ed7i g\u00f3c \u0111\u01b0\u1ee3c t\u00ednh 2 l\u1ea7n, n\u00ean s\u1ed1 g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh l\u00e0: $380 : 2 = 190$ (g\u00f3c) <br\/> Trong $190$ g\u00f3c t\u1ea1o th\u00e0nh c\u00f3 $10$ g\u00f3c b\u1eb9t, n\u00ean s\u1ed1 g\u00f3c kh\u00e1c g\u00f3c b\u1eb9t l\u00e0: $ 190 - 10 = 180$ (g\u00f3c) <br\/> M\u1ed7i g\u00f3c trong 180 g\u00f3c n\u00e0y \u0111\u1ec1u c\u00f3 m\u1ed9t g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh v\u1edbi n\u00f3, <br\/> V\u1eady s\u1ed1 c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh kh\u00e1c g\u00f3c b\u1eb9t l\u00e0. $180 : 2 = 90$ (c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh) <\/span> <br\/><br\/><span class='basic_pink'> \u0110\u00e1p s\u1ed1 l\u00e0 190, 90 <\/span><\/span> <span class='basic_left'><b> L\u01b0u \u00fd <\/b> <br\/> Ta c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh s\u1ed1 g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh t\u1eeb n \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0: n(2n-1) <br\/> S\u1ed1 c\u1eb7p g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh (kh\u00f4ng k\u1ec3 g\u00f3c b\u1eb9t) l\u00e0: n(n - 1) <\/span>"}]}],"id_ques":1527},{"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":[[["50"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":" <span class='basic_left'> Cho g\u00f3c xOy. Tia Oz l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xOy} $. G\u1ecdi Ot l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Ox, Oh l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oz. Cho bi\u1ebft $\\widehat{xOy} = 100^{o} $<br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\widehat{tOh} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-04.png' \/><\/center> Ta c\u00f3 Oz l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{xOy} $ n\u00ean $ \\widehat{xOz} = \\dfrac{\\widehat{xOy}}{2} = \\dfrac{100^{o}}{2} = 50^{o} $ <br\/> M\u1eb7t kh\u00e1c, Ot l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Ox, Oh l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oz <br\/> n\u00ean $\\widehat{tOh} = \\widehat{xOz} = 50^{o} $ (hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh) <br\/> <br\/> <span class='basic_pink'>V\u1eady $ \\widehat{tOh} = 50^{o} $ <\/span><\/span> <br\/><\/span> <br\/><\/span>"}]}],"id_ques":1528},{"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":[[["30"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho bi\u1ebft $\\widehat{AOB} = 120^{o} $. <br\/> Trong g\u00f3c AOB v\u1ebd tia ON sao cho $ON \\perp OB $ <br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\widehat{AON} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-03A.png' \/><\/center> Ta c\u00f3 $ON \\perp OB $ n\u00ean $\\widehat{NOB} = 90^{o} $ <br\/> Tia ON n\u1eb1m trong g\u00f3c AOB n\u00ean: <br\/> $\\widehat{AOB} = \\widehat{AON} + \\widehat{NOB} $ <br\/> $ \\Rightarrow \\widehat{AON} $$ = \\widehat{AOB} - \\widehat{NOB} \\\\ = 120^{o} - 90^{o} \\\\ = 30^{o} $ <br\/> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0: <span class='basic_pink'>30<\/span><\/span> <br\/><\/span> <br\/><\/span>"}]}],"id_ques":1529},{"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":[[["130"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Cho h\u00ecnh v\u1ebd, bi\u1ebft HI \/\/ MP. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-02A.png' \/><\/center> <br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c $\\widehat{IKN} $ l\u00e0: $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^{o} $ ","hint":"","explain":" <span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/hinhhoc/bai7/lv1/img\/H7C17-02B.png' \/><\/center> <br\/> K\u1ebb tia Km \/\/ HI <br\/> $Km \/\/ HI \\\\ HI \/\/ MP $ <br\/> n\u00ean Km \/\/ MP (c\u00f9ng song song v\u1edbi HI) <br\/> $ AB \/\/ Km \\Rightarrow \\widehat{K_{1}} + \\widehat{I} = 180^{o} $ (hai g\u00f3c trong c\u00f9ng ph\u00eda) <br\/> $\\Rightarrow \\widehat{K_{1}}$ $= 180^{o} - \\widehat{I} \\\\ = 180^{o} - 110^{o} \\\\ = 70^{o} $ <br\/> $ Km \/\/ MP \\Rightarrow \\widehat{K_{2}} = \\widehat{N} = 60^{o} $ (hai g\u00f3c so le trong) <br\/> Suy ra $\\widehat{IKN} = \\widehat{K_{1}} + \\widehat{K_{2}} = 70^{o} + 60^{o} = 130^{o} $ <br\/>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0: <span class='basic_pink'> 130 <\/span><\/span> <br\/><\/span> <br\/><\/span>"}]}],"id_ques":1530}],"lesson":{"save":0,"level":1}}