名校
1 . 如图,点
,
,
,
在同一条直线上,点
、
在
的同侧,连接
,
,
,
,
,
,
,试说明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a679040c4d556723e482bacbab41356d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fbb8974a5f907205d26b47b420bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542608b4938fad4da1cd55788887e043.png)
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2 . 某校项目式学习小组开展项目活动,过程如下:
项目主题:测量某水潭的宽度.
问题驱动:能利用哪些数学原理来测量水潭的宽度?
组内探究:由于水潭中间不易到达,无法直接测量,需要借助一些工具来测量,比如自制的直角三角形硬纸板,米尺,测角仪,平面镜等,甚至还可以利用无人机,确定方法后,先画出测量示意图,然后进行实地测量,并得到具体数据,从而计算水潭的宽度.
成果展示:下面是同学们进行交流展示时的两种测量方案:
请你选择上述两种方案中的一种,计算水潭的宽度
.
项目主题:测量某水潭的宽度.
问题驱动:能利用哪些数学原理来测量水潭的宽度?
组内探究:由于水潭中间不易到达,无法直接测量,需要借助一些工具来测量,比如自制的直角三角形硬纸板,米尺,测角仪,平面镜等,甚至还可以利用无人机,确定方法后,先画出测量示意图,然后进行实地测量,并得到具体数据,从而计算水潭的宽度.
成果展示:下面是同学们进行交流展示时的两种测量方案:
方案 | 方案① | 方案② |
测量示意图 | ||
测量说明 | 如图①,测量员在地面上找一点C,在![]() ![]() ![]() | 如图②,测量员在地面上找一点C,沿着![]() ![]() ![]() ![]() |
测量结果 | ![]() ![]() ![]() | ![]() ![]() ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
3 . 如图,在平行四边形
中,
的平分线
交
于点E,
的平分线
交
于点F.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246a86f34603eaf2e6a948681b831b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d16fab0f52c8af5abba0bf19a06ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce1475f537b4ad21775bfaa16daa0c.png)
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2024-03-08更新
|
502次组卷
|
3卷引用:2024年陕西省西安市交通大学附属中学九年级中考一模数学试题
4 . 如图,
,
分别为
轴,
轴的正半轴上的点,作
关于坐标轴的对称线段
和
.
(1)如图(1),若
,
,直接写出点
,
的坐标;
(2)如图,
是
上一点,直线
交
于点
,
.
①如图(2),求证:
;
②如图(3),
平分
交
于点
,交
于点
,若四边形
的面积等于
面积的一半,判断
的形状,并证明你的结论.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/12/677016df-c3c2-4dde-8759-e55b0da4c87b.png?resizew=400)
(1)如图(1),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434845564fd5765244f8d1aa9240fa39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03f416cb4d50a5f473df4bbceeb3094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
①如图(2),求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37325793e54751bf28f15384606688d.png)
②如图(3),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24a8190430bd48d182c911506e74da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-11-08更新
|
163次组卷
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2卷引用:湖北省武汉市江汉区2023-2024学年八年级上学期期中数学试题
5 . 如图,在
中,
,利用尺规在
上分别截取
,使
,分别以D,E为圆心,以大于
的长为半径作弧,两弧在
内交于点F,作射线
交
于点G,若
,过点G作
交
于点P,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674c703e1fee31e92f13ff1923917759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357a3666dbabd00c42fded33d1a0b072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ac49caae8e3b8869d19beeff98966e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65026a6b6402cb599e14be8023a3f6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c42b59b76eafbbe36f13b2daa60132c.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/e4f366453341889fc1c9fc3c3b5ddfce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ca875d563a2fe457e20948b74642cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5634a208294350f8ec151cd19b6d3278.png)
A.2 | B.3 | C.4 | D.5 |
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2023-07-06更新
|
249次组卷
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4卷引用:广东省深圳市坪山区2022~2023学年七年级下学期期末数学试题
广东省深圳市坪山区2022~2023学年七年级下学期期末数学试题(已下线)2023年贵州省中考数学真题变式题7-12题2024年湖南省长沙市立信中学中考二模数学试题(已下线)七年级数学期末模拟卷02(北师大版,一~六章)-学易金卷:2023-2024学年初中下学期期末模拟考试
6 . 如图,
中,
,
,
,垂足为E.
,求
的度数;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fbbd17c89f03dbb61cd6ffdb9a0344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735bd70c2fa2bf51fd7aa448b20d0be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c543c3ddc3723fde6bbfca3ea3b921b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc13fe21e64d9b45614ed43be847904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a997b32c1d78d9a70c76c5605616ae0f.png)
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2023-04-13更新
|
367次组卷
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5卷引用:2023年江苏省无锡梁溪区中考一模数学试题
2023年江苏省无锡梁溪区中考一模数学试题(已下线)专题06 三角形-学易金卷:2023年中考数学一模试题分项汇编(江苏专用)广东省揭阳市榕城区2022-2023学年七年级下学期期末数学试题(已下线)专题04 三角形全等的条件(六大类型)(题型专练)-2023-2024学年八年级数学上册《知识解读·题型专练》(浙教版)(已下线)七年级数学期末模拟卷02(北师大版,一~六章)-学易金卷:2023-2024学年初中下学期期末模拟考试
7 . 如图,已知E,F是平行四边形
对角线
上的点,
.
;
(2)求证:四边形
是平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
(2)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
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2023-08-21更新
|
85次组卷
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3卷引用:湖南省益阳市桃江县2021-2022学年八年级下学期期末数学试题
解答题-问答题
|
较易(0.85)
|
解题方法
8 . 已知
在平面直角坐标系内的位置如图,
,
,
、
的长满足关系式
.
(1)求
、
的长;
(2)求点
的坐标;
(3)在
轴上是否存在点
,使
是以
为腰的等腰三角形.若存在,请直接写出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684e64231777ff5e04c4832eb195bef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9fcc3b010fd1f911c957e0c292bf49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e32076e7b0f2cd720b8487504b6cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80bea26f310543c51ac8fca0f762adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdf5f521bc9b2d2cb3645d56b945226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d5fb153408ee67384916a97b3e7feb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80bea26f310543c51ac8fca0f762adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdf5f521bc9b2d2cb3645d56b945226.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00da8411109f36dc243702d2c11d4974.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2b4e8453eaea35585b37116de3ed94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d994d3118d12d44cdf3a3a5066858b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3942b09e0d0941d4d6d3b1b0f719f8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6487cbefa4d674f6e83c60a88bf806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d994d3118d12d44cdf3a3a5066858b11.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584986928652288/2589980086550528/STEM/eadc3883-13ac-4fc6-b8b1-07d3fb771e12.png?resizew=182)
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2020-11-10更新
|
750次组卷
|
8卷引用:黑龙江省佳木斯市2019-2020学年八年级上学期期末数学试题
黑龙江省佳木斯市2019-2020学年八年级上学期期末数学试题湖北省十堰市房县2020-2021学年八年级上学期期末数学试题陕西省宝鸡市凤翔县2020-2021学年八年级下学期期末数学试题湖北省十堰市郧西县2021-2022学年八年级上学期期末数学试题(已下线)专题1.29 三角形的证明(存在性问题)(基础篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)(已下线)专题13.11 等腰三角形(分层练习)(基础练)-2023-2024学年八年级数学上册基础知识专项突破讲与练(人教版)(已下线)专题2.11 等腰三角形的轴对称性(分层练习)(基础练)-2023-2024学年八年级数学上册基础知识专项突破讲与练(苏科版)广东省惠州市第五中学2022-2023学年八年级上学期期中数学试题