下面是小王同学“过直线外一点作该直线的平行线”的尺规作图过程.
![](https://img.xkw.com/dksih/QBM/2022/4/17/2967088975773696/3000491343323136/STEM/e7c0e5493119460ab8d8233cf3c909af.png?resizew=170)
已知:直线l及直线l外一点P.
求作:直线
,使得
.
作法:如图,
![](https://img.xkw.com/dksih/QBM/2022/4/17/2967088975773696/3000491343323136/STEM/b882143e06cf4a5896f8149b126fd33b.png?resizew=174)
①在直线l外取一点A,作射线
与直线l交于点B,
②以A为圆心,
为半径画弧与直线l交于点C,连接AC,
③以A为圆心,
为半径画弧与线段
交于点Q,
则直线
即为所求.
根据小王设计的尺规作图过程,
(1)使用直尺和圆规,补全图形;(保留作图痕迹)
(2)完成下面的证明.
证明:∵
,
∴
,
(ⅰ)∵
_________,
∴
.
∵
,
,
∴
.
(ⅱ)∴
(____________________).(填推理的依据)
即
.
![](https://img.xkw.com/dksih/QBM/2022/4/17/2967088975773696/3000491343323136/STEM/e7c0e5493119460ab8d8233cf3c909af.png?resizew=170)
已知:直线l及直线l外一点P.
求作:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d10d01d01eb7d3e619e59a48e04982.png)
作法:如图,
![](https://img.xkw.com/dksih/QBM/2022/4/17/2967088975773696/3000491343323136/STEM/b882143e06cf4a5896f8149b126fd33b.png?resizew=174)
①在直线l外取一点A,作射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
②以A为圆心,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
③以A为圆心,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
则直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
根据小王设计的尺规作图过程,
(1)使用直尺和圆规,补全图形;(保留作图痕迹)
(2)完成下面的证明.
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77c8ef75793d21d2d5d8bf470a61159.png)
(ⅰ)∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524f25e1eedbfe399f7f42db890ab89a.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5f8b4e38b11dca682acb0a2fb8eb08.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94abb37fcf526644b9eb04a9afaf7bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0d5d1a7847d111cfe545f5c3c681f1.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ac236a1d0320497a319129dd6c0cd0.png)
(ⅱ)∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66215f352c550586b2c1346a723f20f4.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d10d01d01eb7d3e619e59a48e04982.png)
21-22七年级下·北京海淀·期中 查看更多[2]
北京市海淀区海淀实验中学2021-2022学年七年级下学期期中数学试题(已下线)专题5.11 简单的轴对称图形(等腰三角形)(基础篇)(专项练习)-2022-2023学年七年级数学下册基础知识专项讲练(北师大版)
更新时间:2022-06-13 15:38:10
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