题目内容
如图,如果△ACD∽△ABC,那么下列各式中成立的是( )![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_ST/images0.png)
A.CD2=AD•DB
B.AC2=AD•AB
C.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_ST/0.png)
D.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_ST/1.png)
【答案】分析:利用已知的△ACD∽△ABC,可得相应的比例线段,与答案比较即可得出正确选项.
解答:解:∵△ACD∽△ABC,
∴AC:AD=AB:AC,AD:CD=AC:BC,
∴AC2=AD•AB,CD=
,
=
.
故A错误;B正确;C错误;D错误.
故选B.
点评:本题考查了相似三角形的性质.注意线段的对应.
解答:解:∵△ACD∽△ABC,
∴AC:AD=AB:AC,AD:CD=AC:BC,
∴AC2=AD•AB,CD=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103194827494432876/SYS201311031948274944328002_DA/2.png)
故A错误;B正确;C错误;D错误.
故选B.
点评:本题考查了相似三角形的性质.注意线段的对应.
![](http://thumb2018.1010pic.com/images/loading.gif)
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