小明在学习的过程中,遇到了一个问题:在四边形
中,
,点
是
上一点,且
平分
,
平分
.求证:
.
他的思路是:首先过点
作
的垂线,将其转化为证明三角形全等,然后根据全等三角形的对应边相等,使问题得到解决.请根据小明的思路完成下面的作图与填空:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/12bf1ff0-f3d4-4afd-bcb4-5104b906cf5f.png?resizew=137)
证明:用直尺和圆规,过点
作
的垂线
,垂足为点
(只保留作图痕迹).
,
.
又
,
_____①_____.
平分
,
_____②_____.
又
_____③_____.
_____④_____.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00789287044283e960c443cac80a56f7.png)
.
同理可得_____⑤_____.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d8397018b0a01a1b4e9574604f9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c562adb241caeba188b983f534a489.png)
他的思路是:首先过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/12bf1ff0-f3d4-4afd-bcb4-5104b906cf5f.png?resizew=137)
证明:用直尺和圆规,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc45c88b67f721cb7a09d889659992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e664ab7b7b9c6c6a3078156eccf5f5.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b883e9774dbe058b760adaea21f6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1949518fc246fbd8426d08f701ade25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742973f07cf495cfea658c72b39ed23e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00789287044283e960c443cac80a56f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8d28351f29617ff040f707fed08bb7.png)
同理可得_____⑤_____.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96cb5b56376afb9cae39fef71f2a59.png)
2023·重庆沙坪坝·一模 查看更多[2]
更新时间:2023-05-04 22:13:54
|
相似题推荐
解答题-问答题
|
适中
(0.65)
【推荐1】在
中,
,
,
是过点
的一条直线,
于点
,
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/dc757ee6-c3e5-4b83-828c-7b02030c068c.png?resizew=293)
(1)当直线
处于如图1的位置时,
,
,
具有怎样的数量关系?请写出满足的数量关系,并说明理由:
(2)若直线
处于如图2的位置时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dcbc0a82c2495d16dd1dfcb7bb0e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/dc757ee6-c3e5-4b83-828c-7b02030c068c.png?resizew=293)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce9ecad3d1c6fb02957d23718177114.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在
中,
于点
,
于点
,连结
,
.
是平行四边形;
(2)若
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac18b0388014ae20b2add2975ef56aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ec9d8556300a772755fbbeb0a0e0e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05b9120533f0a342c7dd0f93eb2623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165811055c10ada0e2d73761377ce60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图,在四边形
中,
,
连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/4d087c9e-2c3e-4eab-b48c-c8f751bfbbd8.png?resizew=176)
(1)尺规作图:作线段
的垂直平分线交
于点E,交
于点F,连接
(不下结论、不写作法,保留作图痕迹);
(2)在(1)所作图中,证明四边形
为菱形,完成下列填空.
证明:∵
垂直平分
.
∴ ① ,
∴
.
∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78192b9e9d4e38175e840233749443bd.png)
∴
,
.
∴.
②
∴
.
∴
③ ;即
.
∵
.
∴
.
又∵ ④
∴四边形
是 ⑤
∵
⑥
∴四边形
为菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c9a6255f54f395572a922c801aa490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe2f6543e06a25493855fbbc648be6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78192b9e9d4e38175e840233749443bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/4d087c9e-2c3e-4eab-b48c-c8f751bfbbd8.png?resizew=176)
(1)尺规作图:作线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)在(1)所作图中,证明四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
∴ ① ,
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b5545130a1bd6cdf8fbe8d3ea61b64.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78192b9e9d4e38175e840233749443bd.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fe458fa1cb28c6823bbd09def313af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2ae9575d7c560cab4a539f94f2f4fb.png)
∴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea36aae82612a5c81159ff463163b69.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076a5273440d800b96bfcaaa9970cc45.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c525e0682103065f1ab3ae07b6b8c9e.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c9a6255f54f395572a922c801aa490.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a130e7c109e2196b97e1a76281bf3cf6.png)
又∵ ④
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
【推荐2】如图,在直角坐标系中,先描出点A(1,3),点B(4,1).
(1)描出点A关于x轴的对称点A1的位置,写出A1的坐标 ;
(2)在x轴上找一点C,使AC+BC的值最小,请描出C点的位置;
(3)用尺规在y轴上找一点P,使PA=PB(保留作图痕迹).
(1)描出点A关于x轴的对称点A1的位置,写出A1的坐标 ;
(2)在x轴上找一点C,使AC+BC的值最小,请描出C点的位置;
(3)用尺规在y轴上找一点P,使PA=PB(保留作图痕迹).
![](https://img.xkw.com/dksih/QBM/2021/11/12/2849448767569920/2853438842699776/STEM/bdc0e7cb-5fb8-41d0-b291-b2136ec8e24c.png?resizew=244)
您最近一年使用:0次