如图,在
ABE中,∠EAD = ∠EDA,∠EAC = ∠B.
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834275786956800/2834677849260032/STEM/562cbc00-d715-437d-af4f-c291e07183f8.png?resizew=192)
(1)AD是∠BAC的平分线吗?为什么?
(2)若∠B = 50°,∠E = 40°,求∠ACE和∠BAD的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834275786956800/2834677849260032/STEM/562cbc00-d715-437d-af4f-c291e07183f8.png?resizew=192)
(1)AD是∠BAC的平分线吗?为什么?
(2)若∠B = 50°,∠E = 40°,求∠ACE和∠BAD的度数.
21-22八年级上·四川绵阳·阶段练习 查看更多[2]
四川省绵阳市第二中学2021-2022学年八年级上学期第一次月考试卷数学试题 (已下线)【第三次月考】夯实基础过关卷(考试范围:第十一~十五章)-【冲刺高分】2021-2022学年八年级数学上册培优拔高必刷卷(人教版)
更新时间:2021-10-22 09:09:45
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【推荐1】综合与探究.
数学活动课上,老师组织同学们展开了如下探究:
如图1,
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,
.点D是
边上一点,连接
,以
为直角边作
,其中
,
.
[知识初探]
兴趣小组提出的问题是:“线段
和
有怎样的数量关系和位置关系”,请你直接写出答案_________.
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睿智小组在兴趣小组的基础上,继续探究:如图2,若点D是BC延长线上一点,
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于点F,其它条件不变,线段
和
有怎样的数量关系和位置关系?并说明理由.
[特例探究]
启航小组根据平时的学习经验,“当图形的位置特殊时会产生特殊的数量关系”,在图2的基础上让图形特殊化,如图3,若
平分
,其它条件不变,结果他们发现线段
与
也存在着特殊的数量关系和位置关系.请你直接写出启航小组所发现的正确结果是__________.
[归纳总结]
此综合与实践从“知识初探”“类比再探”到“特例探究”的过程中,主要体现的数学思想是________.(填正确选项代码)
A.数形结合 B.从一般到特殊 C.归纳
数学活动课上,老师组织同学们展开了如下探究:
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.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/03902478df1a55bc99703210bccab910.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/23/156e31ae-31b7-44ef-8e47-9303447280e8.png?resizew=453)
[知识初探]
兴趣小组提出的问题是:“线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
[类比再探]
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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启航小组根据平时的学习经验,“当图形的位置特殊时会产生特殊的数量关系”,在图2的基础上让图形特殊化,如图3,若
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解答题-作图题
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【推荐2】△ABC中,∠C=60°,点D,E分别是边AC,BC上的点,点P是直线AB上一动点,连接PD,PE,设∠DPE=α.
![](https://img.xkw.com/dksih/QBM/2019/8/14/2268604439109632/2268685755793408/STEM/ecae6352202d4cdbbd0b64c826fd7596.png?resizew=329)
(1)如图①所示,如果点P在线段BA上,且α=30°,那么∠PEB+∠PDA=___;
(2)如图②所示,如果点P在线段BA上运动,
①依据题意补全图形;
②写出∠PEB+∠PDA的大小(用含α的式子表示);并说明理由.
(3)如果点P在线段BA的延长线上运动,直接写出∠PEB与∠PDA之间的数量关系(用含α的式子表示).那么∠PEB与∠PDA之间的数量关系是___.
![](https://img.xkw.com/dksih/QBM/2019/8/14/2268604439109632/2268685755793408/STEM/ecae6352202d4cdbbd0b64c826fd7596.png?resizew=329)
(1)如图①所示,如果点P在线段BA上,且α=30°,那么∠PEB+∠PDA=___;
(2)如图②所示,如果点P在线段BA上运动,
①依据题意补全图形;
②写出∠PEB+∠PDA的大小(用含α的式子表示);并说明理由.
(3)如果点P在线段BA的延长线上运动,直接写出∠PEB与∠PDA之间的数量关系(用含α的式子表示).那么∠PEB与∠PDA之间的数量关系是___.
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名校
【推荐1】如图,在
中,
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为等腰三角形.
(2)若
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(2)若
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【推荐2】如图,
是等边三角形,点
、
分别在边
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上,且
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和
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(1)求证:
≌![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0c32d9f3badb7e51233dd39a39fbb3.png)
(2)求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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(1)求证:
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(2)求
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