1 . 如图:
,
,
,
,请问图中
有怎样的数量和位置关系?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5b4ea605cf0b98e428d071f6be6762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6307019d82d2a2a51e0ffd4ebf345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5fc6ead6416492c231c320a5486f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa3115a985b37d25d325836409c7766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e246b559244a543f272e7abf6982007.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/9454e2c4-fd3e-41d7-9298-011a499a68f9.png?resizew=126)
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2 . 如图,B为线段
上一点,以
,
为腰分别作等腰
和等腰
,
,
,
,连接
交
于点F,连接
交
于点G,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/2ae77d71-ce1c-4201-9862-7eef76480e27.png?resizew=190)
(1)求证:
.
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7372745342e507f47de35243c451b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226c231c1150e27c34eb787a46b02ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b4157345e6b5ddee34c82f8e3a3710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/2ae77d71-ce1c-4201-9862-7eef76480e27.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ff124604fe1e16405e9e835f459794.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d98ed618fc3584cdad1936bfd27b6cd.png)
您最近一年使用:0次
2023-12-13更新
|
123次组卷
|
2卷引用:河南省安阳市安阳县2023-2024学年八年级上学期期中数学试题
3 . 如图,点A、D、B、E在同一条直线上,
与
交于点O,已知
,
,
.
;
(2)若
,
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c503e29373e8d87134bdb46bd3912910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47a70a2811c174e73ce1beeb80c75c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b19d7acdcdc8b0eb3ed44729314b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d6f0530c49174047e866dbf2ae1ea4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96807e118c61f9a60e11ccb876cd08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa518d4465a4da299699cfc7d98e3497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9f91270ddbe1cf3c1362e1b95aee14.png)
您最近一年使用:0次
2023-12-12更新
|
85次组卷
|
2卷引用:四川省内江市市中区市中区天立学校2023-2024学年八年级上学期期中数学试题
4 . 如图,
平分
,
的延长线交
于点E,若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1c0d9c74a93c30eefd9c0337e88dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28631e1e4cf1a262fd05b6eb504c0056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6344778ed1e75c1a99e2268468081867.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a35e475a-028e-488c-897e-de825477e1e6.png?resizew=154)
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5 . 如图,是由边长为1的小正方形组成的
网格,
的三个顶点都是格点,且
.仅用无刻度的直尺在给定网格中完成画图,画图过程用虚线表示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/3cc79a25-1641-4bf2-bb0c-953d87f2d005.png?resizew=374)
(1)在图1中,点M是边
与网格线的交点,先作点M关于直线
的对称点
,再在
上画点P,使
;
(2)在图2中,先找格点D,使
,再作
,且点F在
上,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5af85c47a04324701cd91224bfd1e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/3cc79a25-1641-4bf2-bb0c-953d87f2d005.png?resizew=374)
(1)在图1中,点M是边
![](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/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2537e9d8e48196beb661e4ec3b70a7.png)
(2)在图2中,先找格点D,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4004d6308139eddbd1a0458fdd45b41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680b53673467d5e29454148104e32fec.png)
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6 . 在研究三角形中点或中线问题时,常采用延长中线一倍的办法,此法称为:倍长中线.
(1)【原题呈现】八年级上册课本P27:如图①,在
中,
是
边上的中线,点E在
的延长线上,且
.请证明:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/f9ceac8d-5418-4679-8e39-c67f4028e6fe.png?resizew=245)
(2)【思路探究】如图②,已知线段b,c,m.求作:
,使
,
,
边上的中线
.请完善以下作图思路,并填写相应的作图依据.
①已知共顶点两边
,要想作出
,还需要知道
或
.若知道
,则可以根据______作出符合条件的
;若知道
,则可以根据______作出符合条件的
;但目前只知道中线
,所以不能直接作出
.
②根据第(1)题,获得思路.可以作出边为b,c,2m的
.此作图过程需先做出一条线段等于线段m的两倍,然后依据______作出
.
③在
上截取m得
的中点D,连接
并延长至点C,使得______,可得
.
(3)【迁移运用】请根据上述(1)(2)问的证明和思考过程,直接作出满足下列条件的三角形(保留作图痕迹,不写作法 )若用其他思路,作法正确也可以.作等腰
,满足腰
,底边BC上的高
.
(1)【原题呈现】八年级上册课本P27:如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b34233772c4c26d6669499d9b1f15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb0803e134a985e6b444138f75968d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/f9ceac8d-5418-4679-8e39-c67f4028e6fe.png?resizew=245)
(2)【思路探究】如图②,已知线段b,c,m.求作:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df81cda12d7601d58b1d9c7c180c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c884a45b56bc34d79273b067c1520b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3be96420ac78c8621fcb47a45514fa8.png)
①已知共顶点两边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881068127a39caf319492b4177204f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b28f28ced0531d1df34fcf04c6c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b28f28ced0531d1df34fcf04c6c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②根据第(1)题,获得思路.可以作出边为b,c,2m的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
③在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)【迁移运用】请根据上述(1)(2)问的证明和思考过程,直接作出满足下列条件的三角形(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c716b3f1b224bd45eb797f598b895e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29972bb7e1da354a460f22f7516805a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/6bf45a46-3e72-4bf0-a469-bfe10933a598.png?resizew=91)
您最近一年使用:0次
7 . 已知:如图,已知
,
,
为线段
上一点,试说明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4009aa13093cc3865dcd51b371892160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef9500289a895ad4d69f113a11e7525.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/331d55a7-4c78-424a-95b6-21b2d006a6af.png?resizew=138)
您最近一年使用:0次
名校
8 . 如图,已知
,
,
,
,求
的度数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee730f6a2551fb1b582ecf290cfea233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6568df44adc0fb5198810bd50d452b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab41054fa9ce51b68e78d9c0cf398d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a91778530fee017af63165397d36b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fd16f9eca4fef818a8100435abf9e4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/2bfbf18e-d700-4401-aaa2-a3705b572683.png?resizew=181)
您最近一年使用:0次
9 . 如图,在等边
中,
,点P从点A出发沿
边向点B以每秒2个单位的速度移动,点Q从点C出发沿
边向点A以每秒4个单位的速度移动.P,Q两点同时出发,它们移动的时间为t秒.
(1)用含t的代数式表示:
,
;
(2)在点P,Q的运动过程中,是否存在t,使得
与
全等?如果能,请求出t的值;如果不能,请说明理由;
(3)若P、Q两点分别从A、C两点同时出发,并且都按逆时针方向沿
的三边运动,请问经过几秒点P与点Q第一次相遇?并说明相遇的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5685dc4334f1225bc3b62ea645a595d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/3e0d4eca-5155-491d-a583-a408b56022c3.png?resizew=169)
(1)用含t的代数式表示:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524f25e1eedbfe399f7f42db890ab89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbc9c4e4db6374d5ba4c5dec8747442.png)
(2)在点P,Q的运动过程中,是否存在t,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
(3)若P、Q两点分别从A、C两点同时出发,并且都按逆时针方向沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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10 . 如图,在
的正方形网格中,每一个小正方形的边长为
,小正方形的顶点为格点,已知
,
,
,
为格点.
(1)试说明
为等腰三角形.
(2)请你仅用无刻度的直尺,在线段
上求作一点
,使得
,并简单说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89900589ac1333e2a87723c2c4469a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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://img.xkw.com/dksih/QBM/editorImg/2023/11/21/9d9f64ec-9079-4379-869d-69c069fb01ec.png?resizew=122)
(1)试说明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)请你仅用无刻度的直尺,在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650abc501b8d26ec0556b168e9ad20df.png)
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