小王剪了两张直角三角形纸片,进行了如下的操作: 操作一:如图1

小王剪了两张直角三角形纸片,进行了如下的操作:

操作一:如图1,将RtABC沿某条直线折叠,使斜边的两个端点AB重合,折痕为DE

1)如果AC6cmBC8cm,可求得ACD的周长为        

2)如果CADBAD47,可求得B的度数为           

操作二:如图2,小王拿出另一张RtABC纸片,将直角边AC沿直线AD折叠,使它落在斜边AB上,且与AE重合,若AC9cmBC12cm,请求出CD的长.

 


答案

操作一:(114…………2分)

235º…………4分)

操作二:∵AC=9cmBC=12cm

AB===15cm),

根据折叠性质可得AC=AE=9cm

BE=AB-AE=6cm

CD=x,则BD=12-xDE=x

RtBDE中,由题意可得方程x2+62=12-x2

解之得x=4.5

CD=4.5cm…………10分)

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