题型:解答题-证明题
难度:0.65
引用次数:152
题号:22342635
如图,在
中,
,
,
的垂直平分线分别交
和
于点D,E,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/b68f10e1-c8e9-4b2d-bfea-f807d5cf9a3c.png?resizew=92)
(1)求证:
;
(2)连接
,请判断
的形状,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9463cdd7f187734678e4fb53d73b2865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/b68f10e1-c8e9-4b2d-bfea-f807d5cf9a3c.png?resizew=92)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad36ecaddff334dee421d8d40c942836.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
更新时间:2024-04-08 09:38:26
|
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解答题-作图题
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适中
(0.65)
【推荐1】综合与实践:
已知,等腰三角形纸片ABC中,AB=AC,∠BAC=36°.现要将其剪成三张小纸片,使每张小纸片都是等腰三角形(不能有剩余).下面是小文借助尺规解决这一问题的过程,请阅读后完成相应任务.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/65d624dc-3f69-4b2a-9126-2d0ae783abc4.png?resizew=358)
任务:
(1)上述过程中,横线上的结论为_____,括号中的依据为_____.
(2)受小文的启发,同学们想到另一种思路:如图2,以B为圆心,BC长为半径画弧,交AC于点D,交AB于点E.在此基础上构造两条线段(以图中标有字母的点为端点)作为裁剪线,也可解决问题!请在图2中画出一种裁剪方案,直接写出得到的三个等腰三角形及相应顶角的度数.
(3)如图3,等腰三角形纸片ABC中,AB=AC,∠BAC=108°,请从A,B两题中任选一题作答、我选择_____题.
A.请在图3中设计出一种裁剪方案,将该三角形纸片分成三个等腰三角形(要求:尺规作图,保留作图痕迹,不写作法,说明裁剪线).
B.请在图3中设计出一种裁剪方案,将该三角形纸片分成四个等腰三角形,且四个三角形互不全等(要求:尺规作图,保留作图痕迹,不写作法,说明裁剪线).
已知,等腰三角形纸片ABC中,AB=AC,∠BAC=36°.现要将其剪成三张小纸片,使每张小纸片都是等腰三角形(不能有剩余).下面是小文借助尺规解决这一问题的过程,请阅读后完成相应任务.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/29/65d624dc-3f69-4b2a-9126-2d0ae783abc4.png?resizew=358)
作法:如图1所示, ①分别作AB,AC的垂直平分线,交于点P; ②连接PA,PB,PC. 结论:沿线段PA,PB,PC剪开,即可得到三个等腰三角形, 理由:∵点P在线段AB的垂直平分线上, ∴_____(依据). 同理,PA=PC. ∴PA=PB=PC. ∴△PAB、△PBC、△PAC都是等腰三角形 |
(1)上述过程中,横线上的结论为_____,括号中的依据为_____.
(2)受小文的启发,同学们想到另一种思路:如图2,以B为圆心,BC长为半径画弧,交AC于点D,交AB于点E.在此基础上构造两条线段(以图中标有字母的点为端点)作为裁剪线,也可解决问题!请在图2中画出一种裁剪方案,直接写出得到的三个等腰三角形及相应顶角的度数.
(3)如图3,等腰三角形纸片ABC中,AB=AC,∠BAC=108°,请从A,B两题中任选一题作答、我选择_____题.
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B.请在图3中设计出一种裁剪方案,将该三角形纸片分成四个等腰三角形,且四个三角形互不全等(要求:尺规作图,保留作图痕迹,不写作法,说明裁剪线).
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解答题-作图题
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适中
(0.65)
【推荐2】如图,在
的方格纸中,
的顶点均在格点上,请按要求画图.(仅用无刻度的直尺,且不能用直尺的直角,保留作图痕迹)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/3b402bfe-edcf-4d78-a0c1-84f4e67999f3.png?resizew=325)
(1)在图1中,找一格点
,使四边形
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(2)在图2中,在
上作点
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(1)在图1中,找一格点
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在图2中,在
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd260fb9d772c122dcb1df52cbe38ab.png)
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解答题-证明题
|
适中
(0.65)
【推荐1】如图,在
中,
,
平分
,交
于点
,过点
作
于点
.
(1)求证:
;
(2)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6a978e0e798846fee4e8daba0c6fbc.png)
(2)若
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解答题-问答题
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名校
【推荐2】如图1,在边长为
的等边
中,点
从点
出发沿着
以
的速度向点
运动,点
从
点出发沿着
以相同的速度向点
运动,
两点同时出发,设运动时间为
秒.
![](https://img.xkw.com/dksih/QBM/2023/10/17/3348018141822976/3348030700470272/STEM/92cbbffeb2b1495299d6d1c5ee93b632.png?resizew=396)
(1)当
时,试判断
的形状,并说明理由;
(2)当
时,求
的值;
(3)如图2,过点
作
,垂足为
,连接
,以
为边向左作等边
,连接
.
①用含
的代数式表示
的长;
②当
时,
的长度能否为
?若能,求出此时
的长;若不能,请说明理由.
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(1)当
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(2)当
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(3)如图2,过点
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①用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bdbbd3084ddc946e12d530d2192522.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46645cf9b9d1651a149f4bbdde12954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bdbbd3084ddc946e12d530d2192522.png)
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【推荐1】如图,已知△ABC是等边三角形,D为边AC的中点,AE⊥EC,BD=EC,
(1)求证:△BDA≌△CEA;
(2)请判断△ADE是什么三角形,并说明理由.
(1)求证:△BDA≌△CEA;
(2)请判断△ADE是什么三角形,并说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/11c40904-5756-41fc-b9e2-91a8dfd11637.png?resizew=159)
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解答题-作图题
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【推荐2】如图,E是正方形ABCD外一点,且DE=CE=
,连接AE.
(1)将△ADE绕点D逆时针旋转90°
,作出旋转后的图形.
(2)如果∠AED=15°,判断△DEC的形状,并说明理由.
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(1)将△ADE绕点D逆时针旋转90°
![](https://img.xkw.com/dksih/QBM/2018/4/27/1933274792099840/1940188983746560/STEM/662e62116be94e50adb116a82d9bb991.png?resizew=5)
(2)如果∠AED=15°,判断△DEC的形状,并说明理由.
![](https://img.xkw.com/dksih/QBM/2018/4/27/1933274792099840/1940188983746560/STEM/429ca71efd334b6ea153045e01b4de61.png?resizew=197)
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解答题-问答题
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【推荐1】已知四边形ABCD中,AB∥CD,⊙O为内切圆,E为切点.
(Ⅰ)如图1,求∠AOD的度数;
(Ⅱ)如图1,若AO=8cm,DO=6cm,求AD、OE的长;
(Ⅲ)如图2,若F是AD的中点,在(Ⅱ)中条件下,求FO的长.
(Ⅰ)如图1,求∠AOD的度数;
(Ⅱ)如图1,若AO=8cm,DO=6cm,求AD、OE的长;
(Ⅲ)如图2,若F是AD的中点,在(Ⅱ)中条件下,求FO的长.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878935016218624/2879227901616128/STEM/7e25701e75a84ab49656c9adb1ceef8b.png?resizew=383)
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解答题-证明题
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【推荐2】已知:如图,
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