三角形ABC中,BC=6,BC上中线AD=5,P为AD上一点(于A,D不重合),过P作EF//BC,交AB,AC于E,EG//AD,FH//AD1)求证P是线段EF中点 2)当EFGH为菱形时,求EF 3)若sin角ADC=5/6,设AP长为x,四边形EGHF面积为y,求函数解析
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![三角形ABC中,BC=6,BC上中线AD=5,P为AD上一点(于A,D不重合),过P作EF//BC,交AB,AC于E,EG//AD,FH//AD1)求证P是线段EF中点 2)当EFGH为菱形时,求EF 3)若sin角ADC=5/6,设AP长为x,四边形EGHF面积为y,求函数解析](/uploads/image/z/11677614-6-4.jpg?t=%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CBC%3D6%2CBC%E4%B8%8A%E4%B8%AD%E7%BA%BFAD%3D5%2CP%E4%B8%BAAD%E4%B8%8A%E4%B8%80%E7%82%B9%EF%BC%88%E4%BA%8EA%2CD%E4%B8%8D%E9%87%8D%E5%90%88%EF%BC%89%2C%E8%BF%87P%E4%BD%9CEF%2F%2FBC%2C%E4%BA%A4AB%2CAC%E4%BA%8EE%2CEG%2F%2FAD%2CFH%2F%2FAD1%29%E6%B1%82%E8%AF%81P%E6%98%AF%E7%BA%BF%E6%AE%B5EF%E4%B8%AD%E7%82%B9++++++2%EF%BC%89%E5%BD%93EFGH%E4%B8%BA%E8%8F%B1%E5%BD%A2%E6%97%B6%2C%E6%B1%82EF+3%EF%BC%89%E8%8B%A5sin%E8%A7%92ADC%3D5%2F6%2C%E8%AE%BEAP%E9%95%BF%E4%B8%BAx%2C%E5%9B%9B%E8%BE%B9%E5%BD%A2EGHF%E9%9D%A2%E7%A7%AF%E4%B8%BAy%2C%E6%B1%82%E5%87%BD%E6%95%B0%E8%A7%A3%E6%9E%90)
三角形ABC中,BC=6,BC上中线AD=5,P为AD上一点(于A,D不重合),过P作EF//BC,交AB,AC于E,EG//AD,FH//AD1)求证P是线段EF中点 2)当EFGH为菱形时,求EF 3)若sin角ADC=5/6,设AP长为x,四边形EGHF面积为y,求函数解析
三角形ABC中,BC=6,BC上中线AD=5,P为AD上一点(于A,D不重合),过P作EF//BC,交AB,AC于E,EG//AD,FH//AD
1)求证P是线段EF中点 2)当EFGH为菱形时,求EF
3)若sin角ADC=5/6,设AP长为x,四边形EGHF面积为y,求函数解析式和定义域
三角形ABC中,BC=6,BC上中线AD=5,P为AD上一点(于A,D不重合),过P作EF//BC,交AB,AC于E,EG//AD,FH//AD1)求证P是线段EF中点 2)当EFGH为菱形时,求EF 3)若sin角ADC=5/6,设AP长为x,四边形EGHF面积为y,求函数解析
1)∵EF//BC
∴△AEP∽△ABD,△AFP∽△ACD
EP/BD=AP/AD,FP/CD=AP/AD
EP/BD=FP/CD
∵BD=CD
∴EP=FP
2)∵四边形EFGH为菱形
∴EF=EG=PD
∵EF//BC,EG//AD
∴EP/BD=AE/AB,EG/AD=BE/AB
EP/BD+EG/AD=AE/AB+BE/AB=1
1/2EF/(1/2BC)+EF/AD=1
EF/6+EF/5=1
EF=30/11
3)作PQ⊥BC,交BC于Q
∵△AFP∽△FCH∽△ACD
∴S△AFP:S△FCH:S△ACD=AP²:FH²:AD²=x²:(5-x)²:5²
∵S△ACD=1/2AD*CD*sin∠ADC=25/4
∴S△AFP=x²/5²*25/4=x²/4
S△FCH=(5-x)²/5²*25/4=(5-x)²/4
S四边形EFGH=2*(S△ACD-S△AFP-S△FCH)
y=2*[25/4-x²/4-(5-x)²/4]=5x-x² (0
(1)∵EG//AD//FH
EF//GH(EF//BC)
∴四边形EFGH为平行四边形
∴EG=FH
比例性质:
EG/AD=BG/BD
FH/AD=CH/CD
∵BD=CD
∴BG=CH
∴DG=DH
∴PE=PF(2)四边形EFGH为菱形
EF/BC=AP/AD
设EF=FH=GH=EG=x
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