在学习等腰三角形性质时,小美遇到这样一个题目,如图,在
中,
,点D在
边上,连接
.过点C作
于E,且
,求证:
.
垂直
于点F,利用等腰三角形和全等三角形的性质解决问题.请根据小美的思路完成下面的作图与填空.
证明:用直尺和圆规,过点A作
的垂线
,垂足为F.(只保留作图痕迹)
,①______,
.
②______.
③______.
,
④______,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497846628a41a9bc750a645e045afb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a851998b9fb09f51cc0a27db405156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
证明:用直尺和圆规,过点A作
![](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/01b05c9f69a11456689fa92b175c77b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18ba6a737be8d6d9ad6b8dfd0dd9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91f04ceae92ddfaff2d02185bede336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6330150d2742b2536847dea98f377203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc760e5a2ef7ab70237b87b6c0fed979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64479d21c89fa5c1fbcff0f62254e802.png)
更新时间:2024-04-05 10:09:49
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图,
是等边三角形,D是边
上一动点(不与点B,C重合),连接
.点E,F分别在线段
,
的延长线上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/4/fc4800af-d0ec-47cf-9672-30da2a1f09ea.png?resizew=165)
(1)求
的度数;
(2)猜想
与
的数量关系,并证明;
(3)探索当点D从点B运动到点C的过程中,
的周长是否存在最小值?若存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f7f4cb7a4ef888e5235b3ea7cd5d6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/4/fc4800af-d0ec-47cf-9672-30da2a1f09ea.png?resizew=165)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c962fe4f47732b8e6e83d17ff2b9af13.png)
(2)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)探索当点D从点B运动到点C的过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0acc93490a6a784eb62201d93dd93d.png)
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名校
【推荐2】如图,在
中,点E是BC边的中点,连接AE并延长与DC的延长线交于点F.
;
(2)若
,
,
,连接DE,求DE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebb5baea4ac1668b674a8634e15bcbc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18b5e7ad8fde2001e99ae54838adb9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb79c82e2ecee4cce178f5e9d79d39e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
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解答题-问答题
|
适中
(0.65)
【推荐1】如图,在
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1a82fd60-c15d-4fd0-90c9-ffa28723923a.png?resizew=98)
(1)作线段
的垂直平分线交
于点
,交
于点
,要求:不写作法,保留作图痕迹;
(2)连接
,则
的度数为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d777d15cd733338ecfd0ea63819f62c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1a82fd60-c15d-4fd0-90c9-ffa28723923a.png?resizew=98)
(1)作线段
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142544a6d4e6851096afbd3cbad2fe2.png)
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解答题-应用题
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【推荐2】如图,在平面直角坐标系
中,已知
、
是反比例函数
的图像上的两点,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/dcffd758-9e05-48ea-8206-573c0bedbe44.png?resizew=118)
(1)求反比例函数的解析式;
(2)线段
的垂直平分线交
轴于点
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bdb3dac5792ec5fa1ce3f6e7561534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49753619c62e49d6375aa8a7059cbd09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c9940526785ca763da2dfa35e77c934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/dcffd758-9e05-48ea-8206-573c0bedbe44.png?resizew=118)
(1)求反比例函数的解析式;
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解答题-作图题
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适中
(0.65)
【推荐1】数学综合实践课上,李老师在黑板上布置了一道尺规作图题如下:
下面是各个数学小组进行的一系列探究,请你根据探究内容解决问题.
(1)进步小组的作法:以点P为圆心,
长为半径作弧,交⊙
于点B(非点A),作直线
,则直线
即为所求作的切线.问题:
①请你在图(2)中补全进步小组的作图痕迹.
②进步小组通过连接
,
,证明
,他们证明两个三角形全等的依据为______(填“
”“
”或“
”).
(2)希望小组的作法:如图(3),连接
,作
的垂直平分线m交
于点M,以点M为圆心,
长为半径作圆,交
于点B(非点A),作直线
,则直线
即为所求作的切线.
问题:该组的小华根据作图方案给出如下证明过程.
证明:连接
,由作图知,
是
的※,
∴
,(理由:◎)
即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85be38645f49e81c1c754f22ceb10c3.png)
又
是
的半径,
∴
为
的切线.
在上述证明过程中,※处应该填写______;
◎处应该填写______(填序号)
①一条弧所对的圆周角等于它所对的圆心角的一半
②90°的圆周角所对的弦是直径
③直径所对的圆周角是直角
④同弧所对的圆周角相等
(3)拓展小组的作法:如图(4),连接
交
于点C,过点C作
的垂线n,以点O为圆心,
长为半径作弧,交直线n于点D,连接
交
于点B,作直线
,则直线
即为所求作的切线.问题:请你结合该组作图方案给出证明过程.
利用尺规过圆外一点作圆的切线. 已知:如图(1), ![]() ![]() 求作:圆的另一条切线 ![]() ![]() |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/919d147d-f13e-4d94-a675-dacdb827edee.png?resizew=542)
下面是各个数学小组进行的一系列探究,请你根据探究内容解决问题.
(1)进步小组的作法:以点P为圆心,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
①请你在图(2)中补全进步小组的作图痕迹.
②进步小组通过连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395f3eb57b9d06e0e236e751afa11afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a290f047f50481318d040c604d72f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6720e36b02193db161c61d4017673760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9beb8b968744573e593ac28451c69729.png)
(2)希望小组的作法:如图(3),连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
问题:该组的小华根据作图方案给出如下证明过程.
证明:连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ca68d5863d95d52f4d8d7a9e1c5f83.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85be38645f49e81c1c754f22ceb10c3.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
在上述证明过程中,※处应该填写______;
◎处应该填写______(填序号)
①一条弧所对的圆周角等于它所对的圆心角的一半
②90°的圆周角所对的弦是直径
③直径所对的圆周角是直角
④同弧所对的圆周角相等
(3)拓展小组的作法:如图(4),连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
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解答题-作图题
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【推荐2】如图,在△ABC中,∠BAC是钝角,按要求完成下列画图.(不写作法,保留作图痕迹,并分别写出结论)
①用尺规作∠BAC的角平分线AE.
②用三角板作AC边上的高BD.
③用尺规作AB边上的垂直平分线MN.
①用尺规作∠BAC的角平分线AE.
②用三角板作AC边上的高BD.
③用尺规作AB边上的垂直平分线MN.
![](https://img.xkw.com/dksih/QBM/2017/10/8/1790986334552064/1791723536244736/STEM/ac039d21cde64168a0ecd61b6f417732.png?resizew=160)
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解答题-证明题
|
适中
(0.65)
【推荐1】若一条直线经过三角形的一个顶点,且将这个三角形的周长分成相等的两部分,则称这条直线为该三角形的等分线,等分线被这个三角形截得的线段称为该三角形的截径.例如等腰三角形底边上的中线即为它的截径.
(1)若等腰三角形
中,
,过点
的截径长为3,则
.
(2)如图1,四边形
中,
为边
上一点,
,
,过点
作
于点
,求证:直线
为
的等分线;
(3)如图2,
中,
,
,
为
的等分线,
是边
的中点,在
边上求作一点
,使
为
的等分线;
①按题意补全图形(要求:尺规作图,保留作图痕迹,不写作法)
②若
的面积为
,
的面积为
,试直接写出
的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/19/b11fe1ce-036a-416f-bfdf-bebbd4571cdd.png?resizew=372)
(1)若等腰三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284a563413dc0532138fb2a64db8cc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
(2)如图1,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c66f04250c74c6ec60e7b3abdf67c215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2291de85a2a29ff360a4515cce99c804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6cc3789c0e9b7d1226aa0de3327599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
(3)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bb0405afa96ebf94c5b03fd52763dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a33d27a9c655d01f606e9bce02b0a5.png)
①按题意补全图形(要求:尺规作图,保留作图痕迹,不写作法)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a861406a1c1f251aa4df7226c60ce125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1269ea1057c555e256a8ea4a717e0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a025f648f3051e60bb8924dc0bfb313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】如图,在
中,
,点M,N分别以A,C为起点,
/秒的速度沿
边运动,设点M,N运动的时间为t秒(
).
(1)求BC边上的高AE的长度;
(2)连接
,当点t为何值时,四边形
是菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854ec19fca9cce2070c8dc0fa7160dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8383370881922dbedb9a15d2dffff7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f8b27efbbdb6d55e1cd0ce0ef555ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/24/6e732a1f-dd35-4f5a-886d-21a07baddf75.png?resizew=207)
(1)求BC边上的高AE的长度;
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b46010c050239617157231a5c47a777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b977f9880c3acc912c36aa3e2df56c9.png)
您最近一年使用:0次