小明将两个直角三角形纸片如图(1)那样拼放在同一平面上,抽象出如图(2)的平面图形,
与
恰好为对顶角,
,连接
,
,点F是线段
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/4c8d1abb-742b-4411-946a-24ac2abe4305.png?resizew=400)
探究发现:
(1)当点F为线段
的中点时,连接
(如图(2),小明经过探究,得到结论:
.你认为此结论是否成立?_________.(填“是”或“否”)
拓展延伸:
(2)将(1)中的条件与结论互换,即:若
,则点F为线段
的中点.请判断此结论是否成立.若成立,请写出证明过程;若不成立,请说明理由.
问题解决:
(3)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3db3f03c05b28155f9c0d31abfab198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f5e6720c00ee46f8ef8b3417844539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5fc4ad65b723b6a8da4c8dac154e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/4c8d1abb-742b-4411-946a-24ac2abe4305.png?resizew=400)
探究发现:
(1)当点F为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1346a2096399c6e01cce60d0c49af9ca.png)
拓展延伸:
(2)将(1)中的条件与结论互换,即:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1346a2096399c6e01cce60d0c49af9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
问题解决:
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe740243e9ba230fd6922dcc02d6a1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
2020·山东泰安·中考真题 查看更多[9]
山东省泰安市2020年中考数学试题山西省临汾市襄汾县五校联考2020-2021学年九年级上学期期末数学试题(已下线)非选择题专练13 几何探究类—2021年《三步冲刺中考·数学》(全国通用)之第2步大题夺高分2020-2021学年青岛版九年级数学上册第一单元 图形的相似基础卷河南省信阳市罗山县2021-2022学年九年级上学期第三次月考数学试题(已下线)专题27 特殊三角形【考点巩固】-【中考高分导航】备战2022年中考数学考点总复习(全国通用)广西壮族自治区桂林市龙胜各族自治县2022-2023学年九年级上学期期中数学试题湖南省衡阳市常宁市2023-2024学年九年级上学期期末数学试题湖北省黄冈市英山县2023-2024学年九年级下学期月考数学试题
更新时间:2020-07-17 15:25:19
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解答题-问答题
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适中
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【推荐1】如图,在△ABC中,AB=17,BC=21,AD⊥BC交边BC于点D,AD=8,求边AC的长.
![](https://img.xkw.com/dksih/QBM/2021/9/16/2809119082487808/2810970971947008/STEM/8d24a1ae450745efb888caeeae0dc3ab.png?resizew=212)
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解答题-证明题
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适中
(0.65)
【推荐2】如图,在
与
中,
,
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/dc95ad2f-b41c-4e08-9590-adea202f7a02.png?resizew=168)
(1)求证:
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed3163605f3c832ff52779a12f507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692c58a2af64d705cd4a988ed2bfbc3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/dc95ad2f-b41c-4e08-9590-adea202f7a02.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a843875a6ef464532de4c48dab8cbef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0236ebaf869949efb47d7cef6791cebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9af91834644b94e1b023b33e15a0644.png)
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解答题-证明题
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适中
(0.65)
【推荐1】在正方形
中,
是边
上一点(点
不与点
、
重合),连结
.
【感知】如图①,过点
作
交
于点
易证
.(不需要证明)
【探究】如图②,取
的中点
,过点
作
交
于点
,交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/983401e6-97ad-409a-8f7a-da8e68a5503b.png?resizew=300)
(1)求证:
.
(2)连结
,若
,则
的长为______.
![](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/9d78abbad68bbbf12af10cd40ef4c353.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
【感知】如图①,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187ed13a7bd532bd39af5e5ad7493a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af00a2603bb1c492527537d60949c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77245dda9e18f88f43905b192f98758a.png)
【探究】如图②,取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51246bfbcf524ed6da2eceec37712470.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/983401e6-97ad-409a-8f7a-da8e68a5503b.png?resizew=300)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110458927f3f396a5bc27ea4a3b1a3e9.png)
(2)连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee73d637e8260733851b10b322b9cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
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名校
【推荐2】如图,
ABC是等腰直角三角形,∠ACB=90°,点D为斜边AB上一个动点(不与A、B重合)以CD为直角边作等腰直角三角形ECD,∠ECD=90°.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/69fea5b1-678c-4b6c-8c4b-11816bb1e45a.png?resizew=164)
(1)求证:
ACE≌
BCD;
(2)若AB=8,
①AD=3,求DE的长度;
②点D从B到A运动过程中,若DE的中点为P,
BCP的面积是否发生改变?若不变求其值,若变化求出其取值范围.
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/69fea5b1-678c-4b6c-8c4b-11816bb1e45a.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(2)若AB=8,
①AD=3,求DE的长度;
②点D从B到A运动过程中,若DE的中点为P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
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适中
(0.65)
【推荐1】如图,△ABC是一块锐角三角形余料,边BC=120mm,高AD=80mm,要把它加工成正方形零件PQMN,使正方形PQMN的边QM在BC上,其余两个点P,N分别在AB,AC上.求这个正方形零件PQMN面积S.
![](https://img.xkw.com/dksih/QBM/2018/1/1/1850949923913728/1857523212402688/STEM/03e352663c1b4182aa3d466e0a9b57dd.png?resizew=189)
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解答题-证明题
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适中
(0.65)
【推荐2】如图,矩形
中,
,P点从A点出发沿
边以每秒1个单位长度的速度向B点移动,移动时间为t秒,连接
交
于点Q.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/0cc1bffe-5008-4d7b-b05d-04e4c8426337.png?resizew=150)
(1)求证:
;
(2)求当t为何值时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce95ed4820f29d9a3fe8d638c1021a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/17/0cc1bffe-5008-4d7b-b05d-04e4c8426337.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618994d8acda325464cba47fea2db825.png)
(2)求当t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c8e6c6a7c096d0ccb79fa0e2458ce2.png)
您最近一年使用:0次