1 . 如图,在
中,点
分别在边
上,连接
,且
.请从下面三个条件:①
②
;③
中,选择一个合适的作为已知条件,使
为菱形,写出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137717f0e360e82319ced7e3a6c69b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1342725d5ee89770b48a1175dbce82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac679f877d3e3b3acef1f1f8e3654b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b257e4b1c4be85341eb67766c579b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38d97f03faed3152db2fd3bd1919944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08698bd0755e8ba3ead23a944f9399c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
您最近一年使用:0次
名校
2 . 如图,四边形
是平行四边形,
,
是对角线
上的两点,且
.求证:
.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c581dab991aeadf06d972e47673ea8.png)
您最近一年使用:0次
7日内更新
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85次组卷
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34卷引用:2012-2013学年山东省滨州市高新区中学八年级下学期期中质量测试数学试卷
2012-2013学年山东省滨州市高新区中学八年级下学期期中质量测试数学试卷北京市怀柔区2016-2017学年八年级下学期期末质量检测数学试题北京师范大学附属中学2017-2018学年八年级下学期期中考试数学试题山东省东营市胜利第二中学2018-2019学年八年级上学期期末考试数学试题浙江省杭州市第七中学2019届九年级质量综合检测卷数学模拟试卷【校级联考】四川省宜宾市翠屏区中学二片区2018-2019学年八年级下学期半期考试数学试题吉林省伊通满族自治县2018-2019学年八年级下学期期末考试数学试题贵州省毕节市金龙中学2019-2020学年八年级上学期10月月考数学试题贵州省毕节市织金县鸡场中学2019-2020学年八年级上学期10月月考数学试题江苏省镇江市句容市2018-2019学年八年级下学期期中数学试题陕西省商洛市商州区2018-2019学年八年级下学期期中数学试题江苏省沭阳县修远中学2019-2020学年八年级下学期第一次月考数学试题2020年山东省济南市历下区九年级学业水平第一次模拟数学试题2020年山东省济南市历下区中考数学一模试题2019年陕西省西安市长安县第八中学中考数学二模试题山东省济南市历城区2018-2019学年年九年级上学期期末数学试题西藏自治区昌都市2021-2022学年八年级下学期期末数学试题(已下线)9.3 平行四边形-【帮课堂】2022-2023学年八年级数学下册同步精品讲义(苏科版)(已下线)黄金卷03-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷(福建专用)福建省南平市建阳区2022-2023学年八年级下学期期中数学试题福建省永春第一中学2022-2023学年八年级下学期期中考试数学试题广东省汕头市蓝田中学2022-2023学年八年级下学期期中考试数学试卷新疆克孜勒苏柯尔克孜自治州第一中学2022-2023学年八年级下学期期末数学试题湖南省郴州市永兴县树德初级中学2022-2023学年八年级下学期期中数学试题陕西省延安市志丹县2022-2023学年八年级下学期期末数学试题第18章 平行四边形 18.1 平行四边形的性质华东师大版(2012)八年级下册课后作业湖南省永州市第九中学2022-2023学年八年级下学期第一次月考数学试题贵州省铜仁市印江土家族苗族自治县2023-2024学年八年级下学期3月月考数学试题福建省泉州市第一中学2023-2024学年九年级下学期第一次月考数学试题湖北省随州市曾都区2023-2024学年七年级下学期期中数学试题广东省惠州市惠城区合生实验学校2023-2024学年八年级下学期期中数学试题湖南省永兴县树德中学2023-2024学年八年级下学期期中数学试题2024年西藏自治区日喀则市萨迦县中考一模数学试题四川省泸州市泸县百和镇土主中心小学校2023-2024学年八年级下学期4月期中数学试题
真题
3 . 如图,在
中,E,F是对角线
上的点,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d1125b47dec1c5e93143ee59ad862a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
您最近一年使用:0次
4 . 综合与实践:
【课堂探究】在一堂主题为“几何翻折问题的拓展与深化”的数学公开课上,王老师给同学们每个人下发了一张平行四边形纸片,并且给出了一些数据(如图1),并提出,其中平行四边形两边所成的锐角的正切值为
.
(1)为了课堂的顺利进行,王老师先让同学们求出了
_____°;
【实践操作】数学课开始后,王老师让同学们在小组内先动手实践操作,对平行四边形进行翻折探究翻折后图形的性质.在同学们动手实践的过程中,王老师随机挑选了一个小组的操作成果(如图2)并进行展示,接着将其抽象为了一个数学问题.
(2)如图2,在(1)的条件下,点
在
上运动,点
在
上运动,点
为
沿着
翻折后点
的对应点.求证:当M是
中点时,点
落在
边的中线上;
【思考讨论】同学们经过思考后,纷纷给出了自己对于这个问题的看法.王老师非常高兴,继续将问题进行了深入.
(3)如图3,连接
,
,
,延长
至
,连接
,
.若
,
,求证:
平分
;
【学以致用】同学们经过本课的学习,对图形再次进行深入挖掘,在原来的基础上设问:
(4)在(3)的条件下,请直接写出
的正切值.
【课堂探究】在一堂主题为“几何翻折问题的拓展与深化”的数学公开课上,王老师给同学们每个人下发了一张平行四边形纸片,并且给出了一些数据(如图1),并提出,其中平行四边形两边所成的锐角的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
(1)为了课堂的顺利进行,王老师先让同学们求出了
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386cda9f96731510d52ec18199e18286.png)
【实践操作】数学课开始后,王老师让同学们在小组内先动手实践操作,对平行四边形进行翻折探究翻折后图形的性质.在同学们动手实践的过程中,王老师随机挑选了一个小组的操作成果(如图2)并进行展示,接着将其抽象为了一个数学问题.
(2)如图2,在(1)的条件下,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033e44163b3b8e0813685744ee4da07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
【思考讨论】同学们经过思考后,纷纷给出了自己对于这个问题的看法.王老师非常高兴,继续将问题进行了深入.
(3)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab41cce6eb2d3058a644314865d16548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b564c923bdec474b6779a1f8482f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c42c394431e2c46db0936a50efb780a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e52abc8bcfbc43c80b221f60a3e45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356d4349bc0500c3b20b57012a440658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed24d7acba0b3a7ebf4d520296424a3.png)
【学以致用】同学们经过本课的学习,对图形再次进行深入挖掘,在原来的基础上设问:
(4)在(3)的条件下,请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7dca1b3ff383165df0de276308e833.png)
您最近一年使用:0次
名校
5 . 如图,已知四边形
的对角线
、
交于点O,
,
且
.
是菱形;
(2)E为
上一点,连接BE,若
,
,
,求
的长.
![](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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2fb91028cda3644b82b04da29cbe52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0866e1551b61074ca8e61261ecd1f9dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070bc896d35495237fd65576e9b6f88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12323eb1e7bdc938d22c4604142cab84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
您最近一年使用:0次
6 . 如图,在
中,
和
的角平分线
与
交于点
,且点
恰好在边
上.
为
的中点;
(2)点
为
的中点,连接
,交
于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f10681704c4fccfd37664eaf34391dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab1b173dbc2cf639f0bb023c9718b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07302fd45bf77fdd9eca7bc8dbea5e.png)
您最近一年使用:0次
7 . 如图,在平行四边形
中,
是对角线.
的垂直平分线
,分别交
,
,
于点
,
,
,连接
,
(保留作图痕迹,不写作法);
(2)试判断
与
的数量关系,并说明理由.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
8 . 如图,在平行四边形
中,
平分
,交
于点E,
平分
,交
于点F.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c581dab991aeadf06d972e47673ea8.png)
您最近一年使用:0次
9 . 如图,
、
是平行四边形
的对角线
上的两点,且
,
,连接
,
.
.
(2)连接
交
于点
,若
,
,求
的长.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d320f180419175d75eebc618cc458b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17044102f37577b6ee347178945bb70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8157dbcda9476c3e5e113c3d3abc4c6.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5721071f34ec6a6c87c3a8a2b6e822ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916893be8f4f4cf678ecadcef96b9fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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10 . 如图,点E,F是平行四边形
的对角线
上两点,且
,
求证:
.
![](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/90d527b7de54224cc1698843a59a19a5.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b38eae81f97110915792fffc1521b.png)
您最近一年使用:0次