1 . 如图①所示,平行四边形
是某公园的平面示意图.
、
、
、
分别是该公园的四个入口,两条主干道
、
交于点
,请你帮助公园的管理人员解决以下问题:
,
,
,公园的面积为______
;
(2)在(1)的条件下,如图②,公园管理人员在参观了南湖绿道后,为提升游客游览的体验感,准备修建三条绿道
、
、
,其中点
在
上,点
在
上,且
(点
与点
、
不重合),并计划在
与
两块绿地所在区域种植郁金香,求种郁金香区域的面积;
(3)若将公园扩大,此时
,
,
,修建(2)中的绿道每千米费用为
万元,请你计算该公园修建这三条绿道投入资金的是小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61322bc59ed9c2419acf31d42ce4d17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587a938aabb757501d9993943ad22286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f240ba62b73d3609b45bf64d9fd285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa40703e74a4a7bc0e86c75f93fb8ed8.png)
(2)在(1)的条件下,如图②,公园管理人员在参观了南湖绿道后,为提升游客游览的体验感,准备修建三条绿道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7cc44a77f2392abc4cebcae96fbb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bd8b071b24e92e0b1fd38101ffe400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8caca03e0c81d4cd5925ff6b2d576613.png)
(3)若将公园扩大,此时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1dac31fb8c5cd0436e12fde15a9f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f381437732eb14e6beb2dbf1dad0293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7febb6fb174b757e2c1ae2685c53bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
您最近一年使用:0次
名校
2 . 问题提出
(1)如图1,已知点
为线段
上一动点,分别过点
作
,
,连接
. 若
,
,
,则
的最小值为 ;
问题解决
(2)如图2,某公园规划修建一块形如四边形
的牡丹园,其中
,
,
,
,
,
的内心
处修建一个圆形喷水池,公园的入口
是
的中点,
是一条观赏小道,其余部分种植牡丹,现需要在
边上取点
,
上找点
,修建道路
为了节省成本,需要使修建的道路最短,即
的值最小,是否存在这样的点
,使得
的值最小? 若存在,请求出其最小值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/19/9bd8e23a-d34f-4e4d-b6fc-72f1436123d4.png?resizew=424)
(1)如图1,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757942f619e1f8d5296438829fb11b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5daa413c5a1b941452121c5d750a03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e46a7f185146052971adaeb14b3694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18444ec3e5e3b8a0cf488732c34866d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7225d7b261d697f92c76119bc2bd8c0d.png)
问题解决
(2)如图2,某公园规划修建一块形如四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998329f9cdb86f5d60d7d5d70fc3781e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e81e88dbb23b243ce28429ce9e2353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a16dc02090b6e9263555061f14fbc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6483ebae422a8aa8110f65cd61eb7b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54249b32f5db8aab778f03b5774e652f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6a87e27527e02b002e08b53ca27de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54249b32f5db8aab778f03b5774e652f.png)
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3 . 下列说法正确的是( )
A.两点之间,直线最短 | B.圆是立体图形 |
C.小于![]() | D.射线![]() ![]() |
您最近一年使用:0次
2023-06-05更新
|
216次组卷
|
5卷引用:陕西省西安市灞桥区2022-2023学年七年级上学期期末数学试题
陕西省西安市灞桥区2022-2023学年七年级上学期期末数学试题云南省楚雄彝族自治州2022-2023学年七年级上学期期末数学试题云南省楚雄彝族自治州楚雄市2022-2023学年七年级上学期期末数学试题(已下线)4.1 几何初步(题型精讲精练)-【题型分类精粹】2023-2024学年七年级上学期数学期中期末复习讲练系列【考点闯关】(人教版)(已下线)专题07 角与角的比较(七种考法)-【好题汇编】备战2023-2024学年七年级数学上学期期末真题分类汇编(北师大版)
名校
4 . 如图,四边形
中,
,
,
,
,
,点
为直线
左侧平面上一点,
的面积为
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358fc84845695e6eb58ffdf82394a16b.png)
![](https://img.xkw.com/dksih/QBM/2023/5/24/3244468163002368/3245379937525760/STEM/23fc3014c8a54315ab5690680942bb73.png?resizew=162)
您最近一年使用:0次
2023-05-25更新
|
300次组卷
|
2卷引用:2023年陕西省西安高新第一中学中考六模数学试卷
5 . 下列各选项中能用“垂线段最短”来解释的现象是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-05-21更新
|
570次组卷
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19卷引用: 陕西省渭南市大荔县2022-2023学年七年级下学期期末数学试题
陕西省渭南市大荔县2022-2023学年七年级下学期期末数学试题(已下线)专题04 几何初步与三角形-5年(2018-2022)中考1年模拟数学真题分项汇编(河北专用)2023年河北省保定市莲池区中考二模数学试卷湖北省孝感市2022-2023学年七年级下学期期末数学试题湖北省孝感市孝南区2022-2023学年七年级下学期6月期末数学试题广东省河源市东源县2022-2023学年七年级下学期期末数学试题福建省莆田市城厢区莆田哲理中学2023-2024学年七年级上学期期末数学试题(已下线)2022年河北省邢台市九年级下学期中考二模数学试题选填2022年河北省邯郸市九年级中考第二次模拟考试数学试题湖北省十堰市郧阳区2021-2022学年七年级下学期期末数学试题山西省临汾市古县2022-2023学年七年级上学期期末质量监测数学试题江苏省淮安市2023-2024学年七年级上学期期末数学试题河北省邢台市第十九中学2023-2024学年七年级下学期月考数学试题河北省邢台市第二十五中学2023-2024学年七年级下学期第一次月考数学试题辽宁省大连市西岗区第三十七中学2023-2024学年下学期月考数学试卷山东省济南市历城区2023-2024学年七年级下学期期中数学试题广东省江门市新会区葵城中学2023-2024学年七年级下学期期中数学试题河北省邢台经济开发区思源教育集团2023-2024学年七年级下学期月考数学试题(已下线)七年级数学期末模拟卷02(人教版,五~十章)-学易金卷:2023-2024学年初中下学期期末模拟考试
6 . 如图,
中,
,
,
,
,
;垂足分别为点F和E.点G和H分别是
和
上的动点,
,那么
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa30a9ee227af2b387cf6e028c20d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b937442ad4cc480adc11bb143559454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912ec2726c1c57bbc7c2d44e8a674a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1555d23a11970d272f72fa7eb1ffcba8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/9f90a2bb-64f8-4fa4-8163-1fc39d203bc2.png?resizew=191)
您最近一年使用:0次
7 . 如图,直线
平分正方形
的面积,直线
分别与
、
交于点
、
,
直线
于
,连接
,若
,则
长的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39748bd3de9c56dfbe313e65645db6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/df71866a-ea92-485a-88a4-80f4fe883292.png?resizew=161)
您最近一年使用:0次
8 . 如图,在四边形
中,连接
,
与
互余,
、
分别是
、
的中位线,连接
,
,若
,
,则线段
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166c46d68d567af5cc92d33a1540b687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acd79bb9fb06f7c806eb6e17e4b613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/d3c59b4c-170d-4ff1-864f-fe76697b8cfc.png?resizew=272)
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11-12七年级上·湖北省直辖县级单位·期末
9 . 如图,从
到
有多条道路,人们往往走中间的直路,而不会走其他的曲折的路,这是因为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.两条直线相交只有一个交点 | B.两点之间线段最短 |
C.两点确定一条直线 | D.其他的路行不通 |
您最近一年使用:0次
2023-02-21更新
|
243次组卷
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12卷引用:陕西省宝鸡市凤翔师范附属中学2022-2023学年七年级下学期第二次月考数学试题
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10 . 下列说法中正确的有( )
①过两点有且只有一条直线;②连接两点的线段叫两点距离;③两点之间线段最短;④如果
,则点
是
的中点.
①过两点有且只有一条直线;②连接两点的线段叫两点距离;③两点之间线段最短;④如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.2个 | B.3个 | C.4个 | D.5个 |
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