名校
1 . 如图,在
中,
,在三角形内部放一个周长为16的矩形
,使得点E、F在斜边
上,点D、G分别在直角边
上,则矩形的宽
等于( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/a9409b9a-a483-4b4c-b4d0-df3f2c6759a6.png?resizew=198)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21843d70b276f6f35b40870a67c10ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/a9409b9a-a483-4b4c-b4d0-df3f2c6759a6.png?resizew=198)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2 . 如图,在
中,
,
,点
是
的中点,点
是
上一点,
与
交于点
.若
,则
的长为 ___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2d478a257a43d9b28b4105b15e0b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/15/8cff574c-8c78-48c4-a9ec-ade2455f1af3.png?resizew=123)
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3 . 综合与实践
问题情境:
在数学课上,张老师带领同学们以“平移探究”为主题进行教学活动.如图,在菱形纸片
中,
,
,将菱形
沿对角线
剪开,得到
和
,将
沿射线
方向平移一定距离得到
,连接
,
.
(1)如图1,试判断四边形
的形状,并说明理由;
实践探究:
(2)如图2,当四边形
为矩形时,求
平移的距离;
问题拓展:
(3)小颖同学受张老师启发将菱形沿对角线剪开,得到
和
,按如图3方式放置进行平移探究.将
沿
方向平移,连接
,
,并添加条件使得以A、F、C、E为顶点的四边形是一个特殊四边形,请在图4中画出平移后的图形,并写出必要的文字说明.
问题情境:
在数学课上,张老师带领同学们以“平移探究”为主题进行教学活动.如图,在菱形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15ba851a0f65c271ec774095516f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15ba851a0f65c271ec774095516f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5a0a6e5b3f489a7032ea5116c96024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(1)如图1,试判断四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7328ba7a6b4b6764cbe380883fc15f7d.png)
实践探究:
(2)如图2,当四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15ba851a0f65c271ec774095516f07.png)
问题拓展:
(3)小颖同学受张老师启发将菱形沿对角线剪开,得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5a0a6e5b3f489a7032ea5116c96024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
2024-03-31更新
|
125次组卷
|
3卷引用:2024年山西省临汾市洪洞县中考一模数学试题
4 . 如图①,一块材料的形状是锐角三角形
,边
,高
,要把它加工成正方形零件,使正方形的一边在BC上,其余两个顶点分别在边
,
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/1b7c7696-7bf2-4584-a2ac-8df231b1abbf.png?resizew=381)
(1)加工成的正方形零件的边长是多少?
(2)如果原题中要加工成一个矩形零件,且此矩形可由两个大小相同的正方形并排放置组成,如图②,则这个矩形零件的长和宽分别是多少?
(3)图③,如果把这块材料形状改为
的斜板,已知
,
,
,要把它加工成一个形状为平行四边形
的工件,使
在
上,P、N两点分别在
,
上,且
,则平行四边形
的面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf57eef2bac6f23b54d87bd128fac25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b268b2129e91d0af3423f2c001653d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/1b7c7696-7bf2-4584-a2ac-8df231b1abbf.png?resizew=381)
(1)加工成的正方形零件的边长是多少?
(2)如果原题中要加工成一个矩形零件,且此矩形可由两个大小相同的正方形并排放置组成,如图②,则这个矩形零件的长和宽分别是多少?
(3)图③,如果把这块材料形状改为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77df7ac23dd5c286c3b32a45f4791e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a361722688f17c9b8bae311abf6b74a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e5fc12016a63cc49577ffebeab6ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c970f1ff55a73e2e2f77a6b509034950.png)
您最近一年使用:0次
5 . 综合与实践
问题情境:活动课上,同学们以三角形为背景探究图形变化中的数学问题.如图1,
中,
.将
从图1的位置开始绕点C顺时针旋转得到
(点A,B的对应点分别为点
),旋转角为α(
).
操作思考:
(1)如图2,“明辨”小组画出了
恰好经过点B时的图形.求此时旋转角α的度数;
(2)如图3,“善思”小组画出了点
落在
延长线上时的图形,此时点
也恰好在
的延长线上.过点B作
的平行线交
于点P,猜想
和
的数量关系,并说明理由;
拓展探究:
(3)如图4,“博学”小组在图2的基础上,将
沿射线
的方向平移,点B,C,
的对应点分别为D,E,F,若
,当以A,
,D为顶点的三角形是以
为底边的等腰三角形时,请直接写出平移的距离.
问题情境:活动课上,同学们以三角形为背景探究图形变化中的数学问题.如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b185184dc2dc3894a0313fd13f26a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1320d3b30daf11c5a7419983da3b3776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e915c7310f3781887a1afb99dbf949.png)
操作思考:
(1)如图2,“明辨”小组画出了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
(2)如图3,“善思”小组画出了点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
拓展探究:
(3)如图4,“博学”小组在图2的基础上,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def0507ec4fec5f53b5e55d74ba3a3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/25/3f3aa813-d288-4500-aeec-90403e85eef1.png?resizew=561)
您最近一年使用:0次
6 . 如图,已知
的直径
,弦
,
的平分线交
于点
,过点
作
交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/4ecd4faa-5bb4-4448-9f04-bf81b6f9da1a.png?resizew=116)
(1)求证:
是
的切线.
(2)求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/4ecd4faa-5bb4-4448-9f04-bf81b6f9da1a.png?resizew=116)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2012·山西·中考真题
真题
名校
7 . 问题情境:将一副直角三角板(Rt△ABC和Rt△DEF)按图1所示的方式摆放,其中∠ACB=90°,CA=CB,∠FDE=90°,O是AB的中点,点D与点O重合,DF⊥AC于点M,DE⊥BC于点N,试判断线段OM与ON的数量关系,并说明理由.
探究展示:小宇同学展示出如下正确的解法:
解:OM=ON,证明如下:
连接CO,则CO是AB边上中线,
∵CA=CB,∴CO是∠ACB的角平分线.(依据1)
∵OM⊥AC,ON⊥BC,∴OM=ON.(依据2)
反思交流:
(1)上述证明过程中的“依据1”和“依据2”分别是指:
依据1:
依据2:
(2)你有与小宇不同的思考方法吗?请写出你的证明过程.
拓展延伸:
(3)将图1中的Rt△DEF沿着射线BA的方向平移至如图2所示的位置,使点D落在BA的延长线上,FD的延长线与CA的延长线垂直相交于点M,BC的延长线与DE垂直相交于点N,连接OM、ON,试判断线段OM、ON的数量关系与位置关系,并写出证明过程.
探究展示:小宇同学展示出如下正确的解法:
解:OM=ON,证明如下:
连接CO,则CO是AB边上中线,
∵CA=CB,∴CO是∠ACB的角平分线.(依据1)
∵OM⊥AC,ON⊥BC,∴OM=ON.(依据2)
反思交流:
(1)上述证明过程中的“依据1”和“依据2”分别是指:
依据1:
依据2:
(2)你有与小宇不同的思考方法吗?请写出你的证明过程.
拓展延伸:
(3)将图1中的Rt△DEF沿着射线BA的方向平移至如图2所示的位置,使点D落在BA的延长线上,FD的延长线与CA的延长线垂直相交于点M,BC的延长线与DE垂直相交于点N,连接OM、ON,试判断线段OM、ON的数量关系与位置关系,并写出证明过程.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/efdf361a-1817-4e4b-a305-220383ffac72.png?resizew=369)
您最近一年使用:0次
2019-01-30更新
|
1565次组卷
|
13卷引用:2012年初中毕业升学考试(山西卷)数学
(已下线)2012年初中毕业升学考试(山西卷)数学(已下线)【万唯原创】2016年山西-面对面正文-第二部分解答题型6类型1(已下线)【万唯原创】2016年山西中考数学-试题研究-第二部分题型研究 9(已下线)【万唯原创】2014年山西中考数学-试题研究-第二部分 题型研究92014届山东省临沂市九年级中考一模数学试卷2015届四川省乐山市峨边彝族自治县九年级适应性考试数学试卷辽宁省沈阳市第四十四中学2018-2019学年八年级数学上期末试题广西南宁三中初中部2018-2019学年下学期八年级开学考试数学试题内蒙古通辽市科尔沁区2019-2020学年八年级上学期期末数学试题2021-2022学年北师大版八年级下册数学期中复习试题广西壮族自治区南宁市横县2022-2023学年八年级上学期期中数学试题13.3.1 等腰三角形(已下线)数学-2024年中考考前最后一课(10)
8 . 太原汾河四期工程北起尖草坪区上兰村汾河漫水桥(中北大学往南约
米),南至柴村桥北
米处.太原汾河四期的建成,成为市民节假日热门打卡之地.小明和小聪相约游览,他们利用无人机和所学的数学知识对某段河流的宽度
进行了测量.如图所示,小明站在河岸
处测得无人机
的仰角为
,小聪站在小明对面河岸
处测得无人机
的仰角为
,已知小明的身高
,小聪的身高
,无人机
距地面的高度为
(点
,
,
,
,
在同一个平面内).求河流的宽度
.(精确到
。参考数据:
,
,
)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/61a88d13-49b5-4622-8595-bf8951411775.png?resizew=261)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ac61206cb12cf6686bb0facf635010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821b8672d030c240ff230a0174aa7a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1845ed03ec08feac9adee161aab3449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec692d0fed789a952522902815d541b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2088d6fd1c5288253e927aa19b01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03a3794106382223ec07ffd8ab91a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa19eeaf415ed419e77fe92794f443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a49743c3433d9e3d95f5cc0bb87b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3935dc13ab225c9806bef648010c996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e9eaaeea5ab63e69cbc31e488d2cda.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/61a88d13-49b5-4622-8595-bf8951411775.png?resizew=261)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/d70fbad8-5297-4628-9905-7e3a02534eb5.png?resizew=190)
您最近一年使用:0次
9 . 在清明节来临之际,王亮的父亲带王亮自驾车回老家祭拜先祖.用如图所示的方式表示他们回老家的两条路线.设王亮家在A处,老家在D处.第一条是从家出发先向东行驶到达B处,再沿B处的北偏东
方向行驶到达老家D处;第二条是从家向正北方向行驶
到达C处,再沿C处的北偏东
方向到达老家D处.已知车速相同,请说明选择哪条路能更快回到老家.(参考数据:
,
,
)
您最近一年使用:0次
名校
10 . 综合与实践
问题情境:
已知正方形
,点
是
边上一点,将正方形
绕点
顺时针旋转,得到正方形
,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/9088a0a6-0cbb-4a43-b595-697060f8485b.png?resizew=423)
猜想证明:
(1)当
时,如图(1),
①连接
,
,
,求证:四边形
是矩形;
②试猜想线段
,
之间的数量关系,并说明理由.
解决问题:
(2)当
时,
①
______________(用含
的式子表示);
②当
,且点
在
的延长线上时,如图(2),若
,求
的长.
问题情境:
已知正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/9088a0a6-0cbb-4a43-b595-697060f8485b.png?resizew=423)
猜想证明:
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c8dbc31b2e14067ef2f34b4e25f114.png)
①连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2131c5ec585f0cb29c28613011459d8e.png)
②试猜想线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
解决问题:
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c432964f92f710068727d715a7307613.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969c2f53a3e3a4293e36a824b5c7574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
您最近一年使用:0次