如图,在正方形ABCD中,点E是CD边上一动点(点E不与端点C、D重合)AE的垂直平分线FP交AD于F,交CB于G,交AB的延长线于P,H为垂足.(1)当DE/DC=1/3,则AF/AD=____;(2)当DE/DC=1/2时,分别求FH/HG、BP/AB的值;(3)
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![如图,在正方形ABCD中,点E是CD边上一动点(点E不与端点C、D重合)AE的垂直平分线FP交AD于F,交CB于G,交AB的延长线于P,H为垂足.(1)当DE/DC=1/3,则AF/AD=____;(2)当DE/DC=1/2时,分别求FH/HG、BP/AB的值;(3)](/uploads/image/z/2503883-11-3.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E6%AD%A3%E6%96%B9%E5%BD%A2ABCD%E4%B8%AD%2C%E7%82%B9E%E6%98%AFCD%E8%BE%B9%E4%B8%8A%E4%B8%80%E5%8A%A8%E7%82%B9%28%E7%82%B9E%E4%B8%8D%E4%B8%8E%E7%AB%AF%E7%82%B9C%E3%80%81D%E9%87%8D%E5%90%88%29AE%E7%9A%84%E5%9E%82%E7%9B%B4%E5%B9%B3%E5%88%86%E7%BA%BFFP%E4%BA%A4AD%E4%BA%8EF%2C%E4%BA%A4CB%E4%BA%8EG%2C%E4%BA%A4AB%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%8EP%2CH%E4%B8%BA%E5%9E%82%E8%B6%B3.%EF%BC%881%EF%BC%89%E5%BD%93DE%2FDC%3D1%2F3%2C%E5%88%99AF%2FAD%3D____%3B%EF%BC%882%EF%BC%89%E5%BD%93DE%2FDC%3D1%2F2%E6%97%B6%2C%E5%88%86%E5%88%AB%E6%B1%82FH%2FHG%E3%80%81BP%2FAB%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%883%EF%BC%89)
如图,在正方形ABCD中,点E是CD边上一动点(点E不与端点C、D重合)AE的垂直平分线FP交AD于F,交CB于G,交AB的延长线于P,H为垂足.(1)当DE/DC=1/3,则AF/AD=____;(2)当DE/DC=1/2时,分别求FH/HG、BP/AB的值;(3)
如图,在正方形ABCD中,点E是CD边上一动点(点E不与端点C、D重合)AE的垂直平分线FP交AD于F,交CB于G,交AB的延长线于P,H为垂足.
(1)当DE/DC=1/3,则AF/AD=____;
(2)当DE/DC=1/2时,分别求FH/HG、BP/AB的值;
(3)当DE/DC=____时,BP/AB=9/8
过程.
如图,在正方形ABCD中,点E是CD边上一动点(点E不与端点C、D重合)AE的垂直平分线FP交AD于F,交CB于G,交AB的延长线于P,H为垂足.(1)当DE/DC=1/3,则AF/AD=____;(2)当DE/DC=1/2时,分别求FH/HG、BP/AB的值;(3)
如图,∵∠DAE+∠EAB=∠P+∠EAB=90°,
∴∠DAE=∠P,又∵各个垂直,
∴图中所有直角三角形相似.
(1)设AD=6,
∵DE=1/3DC=1/3AD=2,
∴AE=2根号10,AH=根号10,
由AH/AD=AF/AE得AF=10/3,
∴AF/AD=5/9
(2)设AD=4,
∵DE=1/2DC=1/2AD=2,
∴AE=2根号5,AH=根号5,
由AH/AD=HF/DE得HF=根号5/2
由AH²=HF*HP得HP=2根号5,
∴AP=5,BP=1,PG=根号5/2,
∴HG=3根号5/2,
∴HF/HG=1/3,BP/AB=1/4
(3)设DE=2,DE/DC=2/X时,BP/AB=9/8,此时
AD=CD=X,AP=17/8X
∴AE=根号(x²+4),AH=根号(x²+4)/2,
由AH/AP=DE/AE得
[根号(x²+4)/2]/[17X/8]=2/[根号(x²+4)],
化简得2X²-17X+8=0,
解得X1=8,X2=1/2(舍去)
∴当DE/DC=1/4时,BP/AB=9/8
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