1 . 填空:把下面的推理过程补充完整,并在括号内注明理由.
已知:如图,
,
,
,试说明
.
解:∵
(已知)
∴
( )
在
与
中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
∴
( ).
∴
( ).
已知:如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba46f9fceccff74b15e6dad269412cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e6746389305367e7b524ea7aa6e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c10ef52c84726a0a1e9a11c660f921.png)
解:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba46f9fceccff74b15e6dad269412cd.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db07c6ce6c8b0e96a3470c6a3491334.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca10806fc8c3c3efd6859f526b76900.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c10ef52c84726a0a1e9a11c660f921.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/191d2876-688d-4698-8cf9-23973d8062b9.png?resizew=140)
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2 . 如图,
,
均为等腰直角三角形,
,点E在
上,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/882beb62-b5de-4e5e-830e-ea2fd92f28cf.png?resizew=153)
(1)求证:
;
(2)若
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/882beb62-b5de-4e5e-830e-ea2fd92f28cf.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aab54312765518ab2f087aa7a8cb6fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070bc896d35495237fd65576e9b6f88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60634341a9603e24b2bbc6960abe3d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
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3 . 如图,
,
于点
,
于点
,且
,点
从
向
运动,每分钟走
,点
从
向
运动,每分钟走
,
、
两点同时出发,运动( )分钟后,
与
全等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233df632f66ab9266b348076ba72d253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43261d4fafe826d60b8110c8d057cb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1eb58a51aa8dab7d422aa1b332ff64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102fcd5e912a66d13b0d8c2f66813d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/b249c222293a0df29234b4e983ceb11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386f5889ae7aa13ad09b3cdb4f7f89ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbe2dc58818d2f84d0b280cfd16e5d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d8ea93db7e78bd7235fc85e3c4c55a.png)
A.2 | B.3 | C.4 | D.8 |
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4卷引用:贵州省黔南布依族苗族自治州长顺县2022-2023学年八年级上学期期末数学试题
贵州省黔南布依族苗族自治州长顺县2022-2023学年八年级上学期期末数学试题贵州省黔南布依族苗族自治州长顺县2022-2023学年八年级上学期段考数学试题(四)(已下线)专题4.8 图形的全等(基础篇)(专项练习)-2022-2023学年七年级数学下册基础知识专项讲练(北师大版)(已下线)第四章第02讲 图形的全等(5类热点题型讲练)-【帮课堂】2023-2024学年七年级数学下册同步学与练(北师大版)
4 . 如图,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a2ab6940dca62be1f3b2b5f8531990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99020b843d024aa6bd65c053fe9fc37.png)
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|
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3卷引用:河南省三门峡市灵宝市秦岭学校2023-2024学年八年级上学期10月月考数学试题
5 . 如图,为测量桃李湖两端
的距离,南开中学某地理课外实践小组在桃李湖旁的开阔地上选了一点
,测得
的度数,在
的另一侧测得
,
,再测得
的长,就是
的长.那么判定
的理由是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0eadc7cd4adf606107f69775880dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7305de9211785b826823153897b17517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5156cfc49671bff030e170b50141ab.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:江苏省淮安市淮安区周恩来红军中学2023-2024学年八年级上学期10月月考数学试题
江苏省淮安市淮安区周恩来红军中学2023-2024学年八年级上学期10月月考数学试题山东省聊城市阳谷县西湖中学3023-2024学年八年级上学期9月月考数学试题(已下线)专题03 全等三角形的综合应用(五大题型)(题型专练)-2023-2024学年七年级数学下册《知识解读·题型专练》(北师大版)
6 . 下列命题中是真命题的是( )
A.直角三角形的两个锐角互余 |
B.等腰三角形底边上的中线、高线以及顶角的平分线不一定重合 |
C.三角形的一个外角等于两个内角的和 |
D.两个三角形有两条边和一个角分别对应相等,这两个三角形一定全等 |
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7 . 如图,
为
的角平分线,且
,E为
延长线上的一点,
,过E作
,F为垂足,下列结论:①
;②
与
互补;③
;④
.其中正确的是______ .(填序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/bb254c1f-7a63-403a-bf8a-ecf52f34f448.png?resizew=144)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78002bca853929365a3f58082f3e7637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a26c2c53046cbfe83f84f5393373589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958b15afd4f16c2a628f6bfba2b0728d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db866ecc0c098bfc32ec8a43b65bdd58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98de02d1d5b7ac04bce54be393218922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa1b5b6051d500fe6c6f1c19c7ee49f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/bb254c1f-7a63-403a-bf8a-ecf52f34f448.png?resizew=144)
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8 . 两个大小不同的等腰直角三角形
如图所示摆放,点
在同一直线上,连接
.
(1)求证:
.
(2)求证:
.
(3)若
,则
______(直接写出答案).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181cc1d6c57ff0e8f14b6e6a9ebe65d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e8754585a460b01bb92af46cd15b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f243f0482018571a3fcdee60c99b881.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/66b2a76c-6f87-460a-947d-6b2e3bd6d86c.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960d61e0d9a749cba705359a15e683d2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b59bfa454f1729db06a42362086230f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5336ad76763e018ceaec8015b2ca27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ba21720fda641264518b638787454e.png)
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9 . 图①、图②均是4×4的正方形网格,每个小正方形顶点为格点,每个小正方形的边长均为1,点A、B、C均在格点上,按下列要求画图.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/86d792aa-d458-4e34-a080-17785943a175.png?resizew=220)
(1)在图①中,以格点为顶点,
为腰,画一个三边长都是无理数的等腰三角形;
(2)在图②中,找到一个格点D,连接
、
、
,使
与
全等.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/86d792aa-d458-4e34-a080-17785943a175.png?resizew=220)
(1)在图①中,以格点为顶点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在图②中,找到一个格点D,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036191be2322003aaee6bb411868327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
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10 . 如图,已知
,
是线段
上的两点,
,从①
,②
,③
中选择两个作为补充条件,余下的一个作为结论,请写出结论成立的证明过程.
你选的补充条件是______,结论是______.(填序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/9130ca79-555b-421e-92b9-315f653149cf.png?resizew=221)
证明:
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f8eebda19eded2b059774a8c2666c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9b11f2ea112fff1885811bd5bc73cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b4908b37cf23de34d38ae7a0bff278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
你选的补充条件是______,结论是______.(填序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/9130ca79-555b-421e-92b9-315f653149cf.png?resizew=221)
证明:
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