sunfox23
幼苗
共回答了17个问题采纳率:94.1% 举报
(1)5或
![](https://img.yulucn.com/upload/4/7f/47f741d35bc3966e55dd775367dee4b3_thumb.jpg)
;(2)s==24-
![](https://img.yulucn.com/upload/3/22/322a405ce943c4ef08b49ab74d6d3b76_thumb.jpg)
(0<t≤10),s=
![](https://img.yulucn.com/upload/7/47/74702059412358fc220a25af01c3b435_thumb.jpg)
(t>10);(3)
![](https://img.yulucn.com/upload/7/09/709164ed8d3b951dd56ab1e1ac68c6d5_thumb.jpg)
或25s时
试题分析:(1)由直线y=-
![](https://img.yulucn.com/upload/c/e7/ce75439966fd04f39a9f182698394c39_thumb.jpg)
x+8分别交x轴、y轴于点B、点A,可得OB=6,OA=8,则可得AD=t,BE=
![](https://img.yulucn.com/upload/3/04/304501f08d054b3d3f9c27bdd6e12912_thumb.jpg)
t,BD=10-t,由△BDE与△BAO具有公共角∠ABO可得当
![](https://img.yulucn.com/upload/0/cf/0cfbbfd34cbf0ee4fff137b2e2d859bc_thumb.jpg)
或
![](https://img.yulucn.com/upload/3/b7/3b708112707691e577a026d63dc481e9_thumb.jpg)
时两三角形相似,即可求得结果;
(2)①当点D在线段AB上时,先证得△ADF∽△ABO,根据相似三角形的性质可得四边形DFEB为平行四边形,根据平行四边形的性质求解即可;②当点D在AB的延长线上时,四边形OEFD为梯形,
根据梯形的面积公式求解即可;
(3)分①当点D在线段AB上时,②当点D在AB的延长线上时,证得四边形DFEB为平行四边形,根据平行四边形的性质及菱形的判定分析即可.
(1)∵直线y=-
![](https://img.yulucn.com/upload/c/e7/ce75439966fd04f39a9f182698394c39_thumb.jpg)
x+8分别交x轴、y轴于点B、点A,
∴OB=6,OA=8,
则AD=t,BE=
![](https://img.yulucn.com/upload/3/04/304501f08d054b3d3f9c27bdd6e12912_thumb.jpg)
t,BD=10-t,
∵△BDE与△BAO具有公共角∠ABO.
∴当
![](https://img.yulucn.com/upload/0/cf/0cfbbfd34cbf0ee4fff137b2e2d859bc_thumb.jpg)
或
![](https://img.yulucn.com/upload/3/b7/3b708112707691e577a026d63dc481e9_thumb.jpg)
时两三角形相似.
即
![](https://img.yulucn.com/upload/2/10/2108265ab5d223997b971d995fb80cc6_thumb.jpg)
或
![](https://img.yulucn.com/upload/3/74/374a5db50de87603b97bddcd15079be5_thumb.jpg)
,解得t=5或
![](https://img.yulucn.com/upload/4/7f/47f741d35bc3966e55dd775367dee4b3_thumb.jpg)
.
∴当t为5或
![](https://img.yulucn.com/upload/4/7f/47f741d35bc3966e55dd775367dee4b3_thumb.jpg)
时,△BDE与△BAO相似.
(2)①当点D在线段AB上时,
∵DF⊥OA,BO⊥AO,∴DF∥BE,∴△ADF∽△ABO,
∴DF∶BO=AD∶AB=AF∶OA,∴DF=
![](https://img.yulucn.com/upload/a/13/a13eaae04ec1b75dc7b23407fbc28ab2_thumb.jpg)
,AF=
![](https://img.yulucn.com/upload/c/2b/c2bc8840c8f330c3ef8aa230818bf5b3_thumb.jpg)
,
∴BE=DF,∴四边形DFEB为平行四边形,S
△ DEF =S
△ BEF =
![](https://img.yulucn.com/upload/5/2b/52b0ea1988a950167d30e971f0833f7e_thumb.jpg)
S
DFEB ,
∴四边形OFDE的面积等于△BOF的面积,
∴s=
![](https://img.yulucn.com/upload/5/2b/52b0ea1988a950167d30e971f0833f7e_thumb.jpg)
BO·OF=
![](https://img.yulucn.com/upload/5/2b/52b0ea1988a950167d30e971f0833f7e_thumb.jpg)
×6×(8-
![](https://img.yulucn.com/upload/c/2b/c2bc8840c8f330c3ef8aa230818bf5b3_thumb.jpg)
)=24-
![](https://img.yulucn.com/upload/3/22/322a405ce943c4ef08b49ab74d6d3b76_thumb.jpg)
(0<t≤10).
②当点D在AB的延长线上时,四边形OEFD为梯形,
s=
![](https://img.yulucn.com/upload/5/2b/52b0ea1988a950167d30e971f0833f7e_thumb.jpg)
(OE+DF)·OF=
![](https://img.yulucn.com/upload/5/2b/52b0ea1988a950167d30e971f0833f7e_thumb.jpg)
×(
![](https://img.yulucn.com/upload/a/13/a13eaae04ec1b75dc7b23407fbc28ab2_thumb.jpg)
-6+
![](https://img.yulucn.com/upload/a/13/a13eaae04ec1b75dc7b23407fbc28ab2_thumb.jpg)
)×
![](https://img.yulucn.com/upload/c/cc/ccc7d1e0a188b046581930482faf1216_thumb.jpg)
=
![](https://img.yulucn.com/upload/7/47/74702059412358fc220a25af01c3b435_thumb.jpg)
(t>10)
(3)①当点D在线段AB上时,已知四边形DFEB为平行四边形,只需保证BD=BE,即可保证四边形DFEB是菱形,即10-t=
![](https://img.yulucn.com/upload/a/13/a13eaae04ec1b75dc7b23407fbc28ab2_thumb.jpg)
,解得t=
![](https://img.yulucn.com/upload/7/09/709164ed8d3b951dd56ab1e1ac68c6d5_thumb.jpg)
.
②当点D在AB的延长线上时,易证四边形BEFD为平行四边形,只需保证BD=BE,即可保证四边形DFEB是菱形,即t-10=
![](https://img.yulucn.com/upload/a/13/a13eaae04ec1b75dc7b23407fbc28ab2_thumb.jpg)
,解得t=25.
综上所述,当t的值为
![](https://img.yulucn.com/upload/7/09/709164ed8d3b951dd56ab1e1ac68c6d5_thumb.jpg)
或25时,以点D、F、E、B为顶点的四边形是菱形.
点评:此类问题综合性强,难度较大,在中考中比较常见,一般作为压轴题,题目比较典型.
1年前
5