如图,已知
是矩形
的对角线,
,
交
延长线于
,
交
于
,
交
于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/dd356ed0-b8a6-4a00-8376-d2fed7856dc8.png?resizew=182)
(1)求证:点
是
的重心;
(2)如果
,求
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/dd356ed0-b8a6-4a00-8376-d2fed7856dc8.png?resizew=182)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9537d8440750624c628430960595992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a55a1a244f81097e05e715b69580faa.png)
23-24九年级上·上海静安·期末 查看更多[2]
更新时间:2024-01-13 10:37:40
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相似题推荐
解答题-问答题
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【推荐1】阅读与思考:
(1)任务一,在小明的证明过程中,依据1和依据2的内容分别是:
依据1:______________________依据2:______________________
(2)应用
①如图,在
中,点G是
中的重心,连接
并延长交
与点E,若
,求
长.
中,中线
、
相交于点O,若
的面积等于30,求
的面积.
三角形的重心 定义:三角形三条中线相交于一点,这个交点叫做三角形的重心. 三角形重心的一个重要性质: 重心与一边中点的连线的长是对应中线长的 ![]() 下面是小明证明性质的过程. 如图,在 ![]() ![]() ![]() ![]() ![]() ![]() 证明:连接 ![]() ∵D,E是边 ![]() ![]() ∴ ![]() ![]() ∴ ![]() ∴ ![]() ∴ ![]() |
(1)任务一,在小明的证明过程中,依据1和依据2的内容分别是:
依据1:______________________依据2:______________________
(2)应用
①如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d947866d7ee6acc1b59f815ae6a85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4686f39b38d5b90309ee73ed89a0640.png)
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【推荐2】请用无刻度直尺按要求画图,不写画法,保留画图痕迹.(用虚线表示画图过程,实线表示画图结果)
内接于
,
,请在图中画一个含有
圆周角的直角三角形;
(2)如图2,
为
的内接三角形,D是
的中点,E是
的中点,请画出
的角平分线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e702e136211878dce558e0457f15df63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aee6e4e9350a2665df8597ff8045bbd.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/7cbce11aa19b8bd2bf6ee5a834e005de.png)
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【推荐3】发现与探究:三角形的重心
三角形三条中线的交点叫三角形的重心.重心是个物理名词.从效果上看,我们可以认为物体所受重力的合力集中于一点,这一点叫物体的重心.图1,如果取一块均匀的三角形纸板,用一根细线绳从重心O处将三角形提起来,纸板就会处于水平状态.为什么会平衡呢?希望你经过下面的探索过程能得到答案.
图2中,
是
的中线,
与
等底等高,面积相等,记作
.
图3中,若
三条中线
、
、
交于点G,则
是
的中线,利用上述结论可得:
,同理
,
.
,
,
,猜想x,y,z之间的数量关系,并证明你的猜想.
(2)由(1)可知被三条中线分成的六个三角形面积 ,如果
面积为m,用含有m的式子表示
的面积为 ,
=
(3)图4中点D、E在
的边
上,
交于G,G是
重心,
,
,
,求四边形
的面积.
三角形三条中线的交点叫三角形的重心.重心是个物理名词.从效果上看,我们可以认为物体所受重力的合力集中于一点,这一点叫物体的重心.图1,如果取一块均匀的三角形纸板,用一根细线绳从重心O处将三角形提起来,纸板就会处于水平状态.为什么会平衡呢?希望你经过下面的探索过程能得到答案.
图2中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d861b01b8a5410090c4b74ebdfa305c.png)
图3中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffffbccf0eb96123a237860c12a1b892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e3af7996d0c278c131e77df3079e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b937a98f72be529c45af6181e7b219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313ebff25c14192fa0c6c3f72c44f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462161e3839619a52c3b409700a4c337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79f4848fa463200aece2e353e491aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26c8dfbb702045fb71a01e88f1f3545.png)
(2)由(1)可知被三条中线分成的六个三角形面积 ,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdbbc61985b4b1063e0e966de68fbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d457b837e6daf99a33c89197d50e70d4.png)
(3)图4中点D、E在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f279d402050043751e941f3bd7aaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee06d1b67343eac57e4bc24580799c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454328a8e75953fdb0835ce80d9566e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b65d21991c65c735a3d1a502c27cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df4437ed8be04615d252257b30a3a38.png)
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【推荐1】点
为正方形
的边
上任意一点,在正方形内部做等腰直角
.
![](https://img.xkw.com/dksih/QBM/2020/5/21/2467730698657792/2468595948535808/STEM/38f66a5f-7345-4221-ba5b-117cdaae12c0.png?resizew=439)
(1)如图1,若
,则
_________(请直接写出答案)
(2)作
关于
的对称点
,连接
交
于点
.
①补全图形1;
②证明:四边形ECHF为平行四边形.
(3)在(2)的条件下,连接
,请直接写出
和
之间的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8757b210e588f97f856aff20441729d8.png)
![](https://img.xkw.com/dksih/QBM/2020/5/21/2467730698657792/2468595948535808/STEM/38f66a5f-7345-4221-ba5b-117cdaae12c0.png?resizew=439)
(1)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949ff65d3514d6aa7383506030605dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5f441402ee632377b6bedeb060f3d9.png)
(2)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4736c6d7b405a1efeb6a92842a3388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①补全图形1;
②证明:四边形ECHF为平行四边形.
(3)在(2)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4279bbb4cef459f9a49e101073dbc57a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
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【推荐2】如图,在
中,
,
的平分线
,
相交于点
.
在
的平分线上;
(2)连接
,若
,
,
,求点
到
边的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca908463b3d3160bfe72c8395203f7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1bde89afdc3b43070fb7d7612d735c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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【推荐3】3月份,长江重庆段开始进入枯水期,有些航道狭窄的水域通航压力开始慢慢增加.为及时掌握辖区通航环境实时情况,严防船舶搁浅、触礁等险情事故发生,沿江海事执法人员持续开展巡航检查,确保近七百公里的长江干线通航安全.如图,巡航船在一段自西向东的航道上的
处发现,航标
在
处的北偏东45°方向200米处,以航标
为圆心,150米长为半径的圆形区域内有浅滩,会使过往船舶有危险.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2973739464196096/2986467150184448/STEM/c8032f34-f549-435a-997f-b7b0aa526cdb.png?resizew=172)
(1)由于水位下降,巡航船还发现在
处北偏西15°方向300米的
处,露出一片礁石,求
、
两地的距离;(精确到1米)
(2)为保证航道畅通,航道维护项目部会组织挖泥船对该条航道被浅滩影响的航段进行保航施工.请判断该条航道是否被这片浅滩区域影响?如果有被影响,请求出被影响的航道长度为多少米?如果没有被影响,请说明理由.(参考数据:
,
)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2973739464196096/2986467150184448/STEM/c8032f34-f549-435a-997f-b7b0aa526cdb.png?resizew=172)
(1)由于水位下降,巡航船还发现在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)为保证航道畅通,航道维护项目部会组织挖泥船对该条航道被浅滩影响的航段进行保航施工.请判断该条航道是否被这片浅滩区域影响?如果有被影响,请求出被影响的航道长度为多少米?如果没有被影响,请说明理由.(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52881be613aa404e553da30d8987cfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923557f74987174405af890c9a772c48.png)
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【推荐1】如图,已知四边形ABCD为矩形,AD=20cm、AB=10cm.M点从D到A,P点从B到C,两点的速度都为2cm/s;N点从A到B,Q点从C到D,两点的速度都为1cm/s.若四个点同时出发.
(1)判断四边形MNPQ的形状.
(2)四边形MNPQ能为菱形吗?若能,请求出此时运动的时间;若不能,说明理由.
(1)判断四边形MNPQ的形状.
(2)四边形MNPQ能为菱形吗?若能,请求出此时运动的时间;若不能,说明理由.
![](https://img.xkw.com/dksih/QBM/2018/9/25/2040107359264768/2045671372840960/STEM/3ea4750c81fc43a6b776136d8f7d6473.png?resizew=162)
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名校
【推荐2】在等腰
中,
,点P是线段
上动点(与点B,C不重合),连接
,过点C作
交
于点D,在线段
上截取
,过点Q作
交
于点E.
(1)依题意补全图形;
(2)求证:
;
(3)用等式表示线段
与
之间的数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0910601e7d760188d10beee6a48f2ac.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/7210c2fbdb84b991377bf492e29cd8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6030fc53f3eb5500bc9f733d50e72b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/ada4b02b-f8d2-4670-bc14-cdbb01b2661e.png?resizew=133)
(1)依题意补全图形;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b70faeb8cf6c8bdb9aab3a006b4c974.png)
(3)用等式表示线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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解答题-问答题
|
适中
(0.65)
【推荐1】已知:如图,⊙O的半径为3,弦AB的长为4.求sinA的值.
![](https://img.xkw.com/dksih/QBM/2018/3/4/1895118337605632/1895504144359424/STEM/c1396c6141d64d96a924e05e44ff86d6.png?resizew=105)
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▱ABCD中,E是对角线BD上的一点,过点C作CF∥BD,且CF=DE,连接AE,BF,EF.
(1)求证:△ADE≌△BCF.
(2)若∠BFC﹣∠ABE=90°,sin∠ABE=
,BF=4,求BE的长.
(1)求证:△ADE≌△BCF.
(2)若∠BFC﹣∠ABE=90°,sin∠ABE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://img.xkw.com/dksih/QBM/2019/5/30/2214696790974464/2215106233729024/STEM/0420bd21737e46e284d0563783fcf8da.png?resizew=191)
您最近一年使用:0次