1 . 阅读下列材料,并完成相应任务.
镜子里的几何问题
用一面镜子照自己,如果镜子太小,你就看不到自己的整张面孔,换大一点的镜子,你就可以看到整个头部了,如果想看到全身,镜子还得再大一些.那么,到底要多大的镜子才可以呢?可以用数学的思维思考这个问题.如图①,
表示人的高度,
表示镜子里人像的高度,
表示与人相平行的镜面,由平面镜成像原理可知像到镜面的距离等于人到镜面的距离.人与像与镜面都是平行的,E表示人眼睛的位置,易知P是
的中点,Q是
的中点.
是
的中位线,
,要想看到人的全身像,镜子大小最少是人身高的一半.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/1467f3cc-b908-4557-b8b8-ed09d11acd38.png?resizew=445)
(1)材料中P,Q分别为
,
的中点,依据是 .
(2)如图2在(1)的条件下已知小亮身高
米,小亮与镜子
间的距离2米,小明的身高
米,小明与镜子
间的距离为
米,点E为小明眼睛的位置,若小明通过镜子可以看到小亮的全身像,求出此时平面镜的最小高度;
(3)根据镜子中的人像问题请解决如图③,
为直角三角形
,
,点D为
的中点,点P为
上一动点,求
的最小值.
镜子里的几何问题
用一面镜子照自己,如果镜子太小,你就看不到自己的整张面孔,换大一点的镜子,你就可以看到整个头部了,如果想看到全身,镜子还得再大一些.那么,到底要多大的镜子才可以呢?可以用数学的思维思考这个问题.如图①,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eba8ef753df3569875282d12342c149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3a9293c39b2595efa1347c541daa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c073c7d4deabd11bec31c55a75140886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca49c4892a7995633bb46b24470ee40d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/1467f3cc-b908-4557-b8b8-ed09d11acd38.png?resizew=445)
(1)材料中P,Q分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eba8ef753df3569875282d12342c149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3a9293c39b2595efa1347c541daa95.png)
(2)如图2在(1)的条件下已知小亮身高
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8603753eedfcedce65a151b46e7ea700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385f8ed2ee50d16bfa7001bc794c65e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f58f972afae04bbc4549a79efa23aa.png)
(3)根据镜子中的人像问题请解决如图③,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c7d01c3618d579121d95d41a63c565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aaf4388136bd791930647db4bbec217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc817fc4cd7ff4920b2144b6ab5be82.png)
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2 . 如图,点D,E,F在
的边上,
,
.下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/212e8330-7ef3-467a-bec9-0ef868b11701.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75083848b4496b91ddd183a167e6bc2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/212e8330-7ef3-467a-bec9-0ef868b11701.png?resizew=164)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-28更新
|
40次组卷
|
2卷引用:浙江省杭州市临平区2023-2024学年九年级上学期12月月考数学试题
名校
3 . 在
中,
,以
为直径的
分别与
交于点
,过点
作
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/11b9bc2c-4188-4add-9963-ce6d8d9e6b0e.png?resizew=293)
(1)求证:
是
的切线;
(2)如图1,若
的半径为
,求阴影部分的面积;
(3)如图2,若
,求
的值.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887721a843b2dc8e947cc42d09868e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761a77e11e1e45c2a8b2d34d22cf8e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/11b9bc2c-4188-4add-9963-ce6d8d9e6b0e.png?resizew=293)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df79131540626fd835a1fc6ddc9580c.png)
(3)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da68330f025262b33ab806e48ab5c381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-12-25更新
|
225次组卷
|
2卷引用:湖南师大附中博才实验中学2023-2024学年第四次上学期月考数学试题
名校
4 . 已知
,垂足为点O,点E、F分别在射线
、
上,连接
,点A为
的中点,
,
,连接
并延长交线段
或
于点G.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/e8fdacbb-e8d1-426e-8cdd-86573d189acc.png?resizew=380)
(1)如图1所示,当点G在
上,连接
,若
,证明四边形
是矩形;
(2)当点G在
上,请在图2中画出图形并证明
;
(3)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b632ea248b38d73a9e1cfbe700e6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dacca19f76d406c300d549a5a35ce6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/e8fdacbb-e8d1-426e-8cdd-86573d189acc.png?resizew=380)
(1)如图1所示,当点G在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4723f9b49a0851e9211555964f51ba10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1709dcdc54b39f1306b92a6306177d8d.png)
(2)当点G在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea3e9728c725546fcd2854c1c908a97.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b20cd1a43264e4533d4980c99fdad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93401a1551b7e3c5bda0c9bb7220e01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
您最近一年使用:0次
5 . 如图,
,直线
,
与这三条平行线分别交于点A,B,C和点D,E,F.下列结论:①
;②
;③
;④
.其中正确的个数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/28bff1a7-ec68-4630-b247-52eb56004923.png?resizew=141)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96368ee9864da41ef194cbb463f088ba.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/b0f60e9630ea25dbddb2f177ded7a74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babf04cb413242226484695de581b531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15a6b21542a49efbd35456b0d54f6d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd24a3b33b329f33649440940c7c1be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/28bff1a7-ec68-4630-b247-52eb56004923.png?resizew=141)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
6 . 如图,在
中,
,D是
的中点,过点D作
的平行线,交
于点E,作
的垂线,交
于点F.若
,且
的面积为
,则
的长是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17101383eb0787edaaa35adfcd20d5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/b3aeb653-df15-4829-9586-a5e8deee2853.png?resizew=202)
您最近一年使用:0次
2023-12-23更新
|
166次组卷
|
3卷引用:福建省莆田市城厢区莆田哲理中学2023-2024学年九年级上学期月考数学试题
名校
7 . 如图,阳光(平行光线)通过窗户照到厂房内,竖直窗框
在地面上留下2米长的影子
,窗框影子的一端
到窗下墙脚
的距离
为3.6米,窗口底边
与地面的距离
为1.2米.
的长);
(2)如下图,随着平行光线照射角度的变化,窗框影子的一端
沿
向右移动到
,
米,另一端
恰好移动到厂房的另一墙脚
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa69c0b98f245fb9ac28942de982235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a7c635a62b00de7f522a4f9508465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)如下图,随着平行光线照射角度的变化,窗框影子的一端
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37980db411a28c8bf0a3773c8b5d4d14.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2023-12-22更新
|
129次组卷
|
4卷引用:河北省张家口市张北县第三中学2023-2024学年九年级上学期月考数学试题
名校
8 . 如图,抛物线
与x轴交于点A,点
,与y轴交于点C,直线
过点A和点C.
(2)点P是位于直线
上方抛物线上的动点,过点P作x轴的垂线,分别与x轴、
交于点D、E,过点D作
交
于点F,求
的最小值及此时点P的坐标;
(3)在(2)问取得最小值的情况下,将点P向下平移
个单位长度得到点
,将原抛物线y向左平移1个单位长度得到抛物线y,将直线
向右平移9个单位长度得到直线
.设抛物线y与直线
的交点为点M、N(点M在点N的左边),在y轴上是否存在点Q,使得
是以
为腰的等腰三角形?若存在,请直接写出符合条件的点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd275cf054b06be3a3682a6a41af06a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
(2)点P是位于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fda6d76fb350332472e76fefcca6a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace2c179130f74e0a01a9c04c27cf7e4.png)
(3)在(2)问取得最小值的情况下,将点P向下平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1cf820d780b90c8f2425aab6b075ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5a9d54648e191dfc26b16c36b4d0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90e677da86080c7278a34d34ca8e78.png)
您最近一年使用:0次
9 . 下列命题中,真命题的个数是( )
①七边形的内角和是
;
②同行一段路,甲用
小时,乙用
小时,甲乙速度之比为
;
⑧两条直线被一组平行线所截,所得的对应线段成比例;
④若实数
,
满足
,则
.
①七边形的内角和是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10756b4a7a6ed416611fb6dfde986f48.png)
②同行一段路,甲用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb18a3bad840703bcfe819de35ca7584.png)
⑧两条直线被一组平行线所截,所得的对应线段成比例;
④若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5821f59d12217af9a3804379c8231f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
10 . 如图,在
中,
、
分别为
、
的中点,连接
、
、
,
与
相交于点
,则下列结论一定正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/be25bcb0-2785-4a74-baf1-c3f1d9f7f8ea.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/be25bcb0-2785-4a74-baf1-c3f1d9f7f8ea.png?resizew=137)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次