Bài 15: Cho tam giác ABC vuông tại A, có AC = 20 cm; AB = 15 cm. Gọi M là trung điểm của cạnh BC. Tính độ dài đoạn thẳng MA.
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 5:
Ta có: \(AB^2=BH\cdot BC\)
\(\Leftrightarrow BH\left(BH+9\right)=400\)
\(\Leftrightarrow BH^2+25HB-16HB-400=0\)
\(\Leftrightarrow BH=16\left(cm\right)\)
hay BC=25(cm)
Xét ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC
nên \(\left\{{}\begin{matrix}AC^2=CH\cdot BC\\AH\cdot BC=AB\cdot AC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AC=15\left(cm\right)\\AH=12\left(cm\right)\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,\widehat{B}+\widehat{C}=90^0\left(tg.ABC\perp A\right)\\ \Rightarrow\widehat{B}=90^0-60^0=30^0\\ 2,\tan\widehat{C}=\dfrac{AB}{AC}=\tan60^0=\sqrt{3}\Leftrightarrow AB=15\sqrt{3}\left(cm\right)\\ 3,BC=\sqrt{AB^2+AC^2}=30\left(cm\right)\left(pytago\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
bài 9
tam giác ABC vuông tại A có
* BC2=AB2+AC2
BC2=152+202=625
BC=25cm
* AH.BC=AB.AC
AH.25=15.20
AH.25=300
AH=12cm
tam giác ABH vuông tại H có
BH2=AB2-AH2
BH2=152-122=81
BH=9cm
tam giác ABC vuông tại A có
*AB2=BH.BC
225=9.BC
BC=25cm
CH=BC-BH=25-9=16cm
*AC2=BC2-AB2
AC2=252-152=400
AC=20cm
![](https://rs.olm.vn/images/avt/0.png?1311)
1: Xét ΔABC vuông tại A và ΔHAC vuông tại H có
góc ACB chung
Do đó: ΔABC\(\sim\)ΔHAC
2: \(BC=\sqrt{AB^2+AC^2}=25\left(cm\right)\)
Xét ΔABC có AM là phân giác
nên BM/AB=CM/AC
=>BM/3=CM/4
Áp dụng tính chất của dãy tr số bằng nhau, ta được:
\(\dfrac{BM}{3}=\dfrac{CM}{4}=\dfrac{BM+CM}{3+4}=\dfrac{25}{7}\)
Do đó: BM=75/7(cm); CM=100/7(cm)
a) ABC có
MA = MB ( gt )
NB = NC ( gt )
=> MN là đường trung bình của
ABC
=> MN =
AC =
.20 = 10 ( cm )
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=>![B C space equals space square root of A B squared space plus thin space A C squared end root
space space space space space space equals space root index blank of 15 squared space plus thin space 20 squared end root](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2256%22%20width%3D%22149%22%20wrs%3Abaseline%3D%2227%22%3E%3C!--MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmsqrt%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%26%23x2009%3B%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmsqrt%3E%3Cmspace%20linebreak%3D%22newline%22%2F%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmroot%3E%3Cmrow%3E%3Cmsup%3E%3Cmn%3E15%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%26%23x2009%3B%3C%2Fmo%3E%3Cmsup%3E%3Cmn%3E20%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmrow%2F%3E%3C%2Fmroot%3E%3C%2Fmath%3E--%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A'math1564b4c0e54101ac57a0cb68c16'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABK2hlYWQQC2qxAAACwAAAADZoaGVhCGsXSAAAAvgAAAAkaG10eE2rRkcAAAMcAAAADGxvY2EAHTwYAAADKAAAABBtYXhwBT0FPgAAAzgAAAAgbmFtZaBxlY4AAANYAAABn3Bvc3QB9wD6AAAE%2BAAAACBwcmVwa1uragAABRgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACACsAPf%2F%2FAAAAKwA9%2F%2F%2F%2F1v%2FFAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAEAgABVAtUCqwALAEkBGLIMAQEUExCxAAP2sQEE9bAKPLEDBfWwCDyxBQT1sAY8sQ0D5gCxAAATELEBBuSxAQETELAFPLEDBOWxCwX1sAc8sQkE5TEwEyERMxEhFSERIxEhgAEAVQEA%2FwBV%2FwABqwEA%2FwBW%2FwABAAACAIAA6wLVAhUAAwAHAGUYAbAIELAG1LAGELAF1LAIELAB1LABELAA1LAGELAHPLAFELAEPLABELACPLAAELADPACwCBCwBtSwBhCwB9SwBxCwAdSwARCwAtSwBhCwBTywBxCwBDywARCwADywAhCwAzwxMBMhNSEdASE1gAJV%2FasCVQHAVdVVVQAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%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%3D%3D)format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2222%22%3EB%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2222%22%3EC%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1564b4c0e54101ac57a0cb68c16%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2236.5%22%20y%3D%2222%22%3E%3D%3C%2Ftext%3E%3Cpolyline%20fill%3D%22none%22%20points%3D%2212%2C-20%2011%2C-20%205%2C0%202%2C-8%22%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20transform%3D%22translate(49.5%2C23.5)%22%2F%3E%3Cpolyline%20fill%3D%22none%22%20points%3D%225%2C0%202%2C-8%200%2C-7%22%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20transform%3D%22translate(49.5%2C23.5)%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2261.5%22%20x2%3D%22147.5%22%20y1%3D%223.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2268.5%22%20y%3D%2222%22%3EA%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2279.5%22%20y%3D%2222%22%3EB%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2212%22%20text-anchor%3D%22middle%22%20x%3D%2289.5%22%20y%3D%2215%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1564b4c0e54101ac57a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= 25 cm
AN là đường trung tuyến ( NB = NC )
=> AN =
=
= 12,5 ( cm ))
b) ABDC có 2 đường chéo AD , BC cắt nhau tại N
mà CN = ND ( gt )
AN = ND ( gt )
=> ABDC là hình bình hành
mà![stack C A B with hat on top space equals space 90 degree](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2223%22%20width%3D%2287%22%20wrs%3Abaseline%3D%2219%22%3E%3C!--MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%5E%3C%2Fmo%3E%3C%2Fmover%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmn%3E90%3C%2Fmn%3E%3Cmo%3E%26%23xB0%3B%3C%2Fmo%3E%3C%2Fmath%3E--%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A'math123919e9c7f188e0f3ae690e7e2'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAABTGhlYWQQC2qxAAAC4AAAADZoaGVhCGsXSAAAAxgAAAAkaG10eE2rRkcAAAM8AAAADGxvY2EAHTwYAAADSAAAABBtYXhwBT0FPgAAA1gAAAAgbmFtZaBxlY4AAAN4AAABn3Bvc3QB9wD6AAAFGAAAACBwcmVwa1uragAABTgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACAD0AsP%2F%2FAAAAPQCw%2F%2F%2F%2FxP9SAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgADrAtUCFQADAAcAZRgBsAgQsAbUsAYQsAXUsAgQsAHUsAEQsADUsAYQsAc8sAUQsAQ8sAEQsAI8sAAQsAM8ALAIELAG1LAGELAH1LAHELAB1LABELAC1LAGELAFPLAHELAEPLABELAAPLACELADPDEwEyE1IR0BITWAAlX9qwJVAcBV1VVVAAIAVQHWAasDKwALABcASRgBsBgQsQgF9LESBfSxDwX0sQwF9LECBfSxGQX0swsVBQ8QPDw8ALAYELELAvSxDwX0sRIF9LEVBfSxBQX0swgMAhIQPDw8MDEAFhUUBiMuATc0Nh8BNCYjJgYVFBYXMjYBVlVVVlVWAVVVVSorKisrKisqAypVVVVVAVRWVVUBqisqASorKyoBKgABAAAAAQAA1XjOQV8PPPUAAwQA%2F%2F%2F%2F%2F9Y6E3P%2F%2F%2F%2F%2F1joTcwAA%2FyAEgAOrAAAACgACAAEAAAAAAAEAAAPo%2F2oAABdwAAD%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%2F)format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%2218.5%22%20y1%3D%225.5%22%20y2%3D%223.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2218.5%22%20x2%3D%2234.5%22%20y1%3D%223.5%22%20y2%3D%225.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%226.5%22%20y%3D%2219%22%3EC%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2219%22%3EA%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2228.5%22%20y%3D%2219%22%3EB%3C%2Ftext%3E%3Ctext%20font-family%3D%22math123919e9c7f188e0f3ae690e7e2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2219%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2219%22%3E90%3C%2Ftext%3E%3Ctext%20font-family%3D%22math123919e9c7f188e0f3ae690e7e2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2282.5%22%20y%3D%2219%22%3E%26%23xB0%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
=> ABDC là hình chữ nhật
*(Cho mình 1 nút like vs bn ơi )