(1)在一次数学活动课上,老师让同学们用两个大小、形状都相同的三角板画平行线
、
,并说出自己做法的依据.小琛、小萱、小冉三位同学的做法如下:
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974417360732160/2977770719772672/STEM/d0692d93-2b23-41ec-a38d-f25b62502f85.png?resizew=473)
小琛说:“我的做法的依据是内错角相等,两直线平行”
①小琛说的是否正确?________(回答正确或错误)
②小萱做法的依据是________________________;
③小冉做法的依据是________________________.
(2)如图,如果
,
,
,那么
与
平行吗?
与
呢?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974417360732160/2977770719772672/STEM/d0692d93-2b23-41ec-a38d-f25b62502f85.png?resizew=473)
小琛说:“我的做法的依据是内错角相等,两直线平行”
①小琛说的是否正确?________(回答正确或错误)
②小萱做法的依据是________________________;
③小冉做法的依据是________________________.
(2)如图,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee4e0de0c1de0835766b7f627f348c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8892182595abb470943ea5d90aedafc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4d00b86b2f067b902baf6e52f0faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974417360732160/2977770719772672/STEM/622daccf-4a11-4e0c-ab7f-621f50a50992.png?resizew=233)
21-22七年级下·河南许昌·期中 查看更多[5]
河南省许昌市长葛市2021-2022学年七年级下学期期中数学试题(已下线)专题1.3 平行线的判定-【帮课堂】2022-2023学年七年级数学下册同步精品讲义(浙教版)(已下线)第五章 相交线与平行线 章末检测卷-2022-2023学年七年级数学下册重难题型全归纳及技巧提升专项精练(人教版)湖北省仙桃市荣怀学校2022-2023学年七年级下学期第一次学业水平检测数学试题山西省大同市第一中学校2022-2023学年七年级下学期数学阶段性综合素养评价(一)
更新时间:2022-05-12 13:12:56
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解答题-作图题
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【推荐1】如图:点B是∠DAC边AC上一点,用尺规作出直线BE,使BE∥AD.
(要求:使用尺规正确作图,保留作图痕迹)
(要求:使用尺规正确作图,保留作图痕迹)
![](https://img.xkw.com/dksih/QBM/2019/5/3/2195702398509056/2197688579162112/STEM/b1b4d1d44cac4b4ea5c9c39449366ab4.png?resizew=133)
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解答题-证明题
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【推荐2】补全下面推理过程
如图,
平分
.
与
平行吗?请说明理由;
解:
与
______,理由如下:
,(平角的定义)
,(已知)
______(______),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8644afba5451902a1d517ec584877a.png)
(2)
与
的位置关系如何?为什么?
解:
与
的位置关系是:______.
平分
;(已知)
(______),
又
(已知).
即
,
______(______).
(______).
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be0388b68e40772721ca4221adf880e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5457071c703edd0ec7ef0a250a0fda05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
解:
![](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/68758941f4a7ce22b3aab6000e5cd4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f10e367216271375ec17a83bc5a3ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf6a2fe4ad6f0f4f7944b06c04fa581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8644afba5451902a1d517ec584877a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85f511236e5645290b9d06984558ea0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a92a6b49d03eb1afd3e218e1ee4db5.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb798764cb88423096ec3fcd11e68f68.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89952563bf758b6e7a6c7dd28d1767a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de65cc0b0f12fc65237bddf3d3f0cf8e.png)
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【推荐2】如图,E、F是四边形
对角线
上两点,
,
.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/60ef95894ceebaf236170e8832dcf7e3.png)
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解答题-证明题
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【推荐1】请结合题意,在横线上填上合适的推理依据.
如图,
,
,求证:
.
(已知)
∴
(垂直的定义)
∵
(已知)
∴______
______(____________________)
∴
______(____________________)
又∵
(已知)
∴
(____________________)
∴
(____________________)
∴
(两直线平行,同位角相等)
∴
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc0613441dac089635db3d6efd4aeb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb21db3e4ef86d2b044d76dcbc8ff27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a389e0b0232e986d1c341b45e5b28e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc0613441dac089635db3d6efd4aeb4.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0445e750c0443f25e29a081103780b3b.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/286741032e16d3ea51ee74cbad54d195.png)
∴______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84123d56994a7416790420fedd81b745.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e96f7f27f5364368b21c2d9fc68ead0.png)
∴
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∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3255ac1b6f934fcb4aa742a81bd8aef6.png)
∴
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∴
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解答题-证明题
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【推荐2】如图,三角形
中,
是
上一点,
是
上一点,点
,
在
上,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/10/99dd8dc7-4925-4eed-a126-610feb6e99d8.png?resizew=184)
(1)求证:
;
(2)若
,
平分
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/10/99dd8dc7-4925-4eed-a126-610feb6e99d8.png?resizew=184)
(1)求证:
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(2)若
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解答题-作图题
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【推荐2】已知:如图,BD⊥AC于点D,点E是线段BC上的任意一点(不与点B,C重合),过点E作EF⊥AC于点F,过点D作DG
BC交AB于点G.
![](https://img.xkw.com/dksih/QBM/2022/7/12/3021018347560960/3025342099210240/STEM/1fb27d1867454af29bb2c36dcd0360ac.png?resizew=191)
(1)①请补全图形;
②求证:BD
EF;
(2)用等式表示∠GDB与∠C的数量关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://img.xkw.com/dksih/QBM/2022/7/12/3021018347560960/3025342099210240/STEM/1fb27d1867454af29bb2c36dcd0360ac.png?resizew=191)
(1)①请补全图形;
②求证:BD
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
(2)用等式表示∠GDB与∠C的数量关系,并证明你的结论.
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