1 . 数学实践活动是一种非常有效的学习方式,通过活动可以激发学习兴趣,提高动手动脑能力,拓展思维,改进学习方法,提高学习效率.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/b6c81236-accc-4a27-a692-0f0754cb9fb2.png?resizew=352)
(1)发现解决:将正方形纸片
折叠,使边
都落在对角线
上,展开得到折痕
如图①,则
_________;线段
之间的数量关系为________;
(2)类比引申:如图②,在矩形
中,连接对角线
,E是
上的一点,四边形
是正方形,如果
,则矩形
的面积是多少?
(3)拓展应用:如果图①中正方形纸片
的边长为4,沿
剪开,再进行折叠,使
的边
重合,折痕为
.点P,点Q在边
上,
,连接
,如图③,则
的周长是多少?
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/b6c81236-accc-4a27-a692-0f0754cb9fb2.png?resizew=352)
(1)发现解决:将正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210830766989a07c24b05589007aebbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968b2adc9dd770e5994569a459a2d659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e569f82eb96d237501ed0fba536e9ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a45bb0e736a231e0179772a5c036124.png)
(2)类比引申:如图②,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d819c261ee68e705e0d71815a050b7aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd25db1459848a1c1f799b29ac6d6bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)拓展应用:如果图①中正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667f534c3893e5dcfe16be356202971a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667f534c3893e5dcfe16be356202971a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54edadd93c68b0105da2dccc8c3f410c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
您最近一年使用:0次
2 . 【问题背景】
(1)如图1,在等边
中,点
,
分别为边
,
上的点,
,
,求
的值;
【迁移应用】
(2)如图2,在
中,
,
,点
为
的中点,点
,
分别为边
,
上的点,
,
,
,求
的面积;
【拓展延伸】
(3)如图3,在
中,
,
,
,点
,
分别为边
,
上的点,
,
,求
的长.
(1)如图1,在等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d40d5cb59338d3cb1dd504bb12d107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91afde1c60057fa19be31e8f852f2cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcda8436a5e68816b74177e6d51cba7.png)
【迁移应用】
(2)如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345c91c9e67e6ee00a872078ab17f094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c39e22f3eda6e52e6461fb8b548d464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
【拓展延伸】
(3)如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c99fc553ecb3e2afdb7058201bc642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0af13586681abc06d8b41fab349294ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d2231c7a2875ab6d423dff3ead4069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
名校
3 . 如图1,在
中,
,
,点
、
分别在边
、
上,
,连接
.将
绕点
顺时针方向旋转,记旋转角为
.
(1)[问题发现]
①当
时,
______;
②当
时,
的值是多少?请给出证明过程.
(2)[拓展研究]
试判断:当
时,
的大小有无变化?请仅就图2的情形给出证明;
(3)[问题解决]
在旋转过程中,
的最大值是多少?请直接写出答案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630d82ae0ed6deb825514e0bc92e74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ceb3cc7e4c368c7b13a65d463f3c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/361973e9-54ef-4d87-982f-b05466adc897.png?resizew=421)
(1)[问题发现]
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469451242301adbf795110cbb9154403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc00342101809b43c1c3187dc0d06f9b.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cb3cc93e355ace2adee68be0a068f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1672bf7cfa9a741651889f41855f6f3b.png)
(2)[拓展研究]
试判断:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef047d4e8392c80f84689e659a7a98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1672bf7cfa9a741651889f41855f6f3b.png)
(3)[问题解决]
在旋转过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2023-12-09更新
|
97次组卷
|
6卷引用:2024年贵州省中考数学模拟预测试题
4 . 小波在复习时,遇到一个课本上的问题,温故后进行了操作、推理与拓展.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/abbe942d-a225-4443-9862-167821dc5a6c.png?resizew=472)
(1)温故:如图①,在
中,
于点
,正方形
的边
在
上,顶点
,
分别在
,
上,若
,
,求正方形
的边长(用
,
表示),
(2)操作:如何画出这个正方形
呢?
如图②,小波画出了图①的
,然后按数学家波利亚在《怎样解题》中的方法进行操作:先在
上任取一点
,画正方形
,使点
,
在
边上,点
在
内,然后连接
,并延长交
于点
,画
于点
,
交
于点
,
于点
,得到四边形
;
(3)推理:证明图②中的四边形
是正方形;
(4)拓展:小波把图②中的线段
称为“波利亚线”,在该线上截取
,连接
,
(如图③),当
时,求“波利亚线”
的长(用
,
表示).
请帮助小波解决“温故”、“推理”、“拓展”中的问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/abbe942d-a225-4443-9862-167821dc5a6c.png?resizew=472)
(1)温故:如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](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/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d22f065ec04de109d913e8e7855110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(2)操作:如何画出这个正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
如图②,小波画出了图①的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca9581c221aa3016b035444015a7e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d486055c508b9ff7f79fb8d2a464458b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dacd0086635538bf42d08bfdaf481cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2c2bfe8c8337ca8f2fba6af5fddec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f24325565a9dd95128a633a240da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(3)推理:证明图②中的四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(4)拓展:小波把图②中的线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df7c43dd51ecde238a068b8138e8b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e33bc76f589215d9738bfc3988bfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
请帮助小波解决“温故”、“推理”、“拓展”中的问题.
您最近一年使用:0次
5 . 如图甲,正方形
和等腰直角
有公共点
,点
是直线
上一动点,连接
,取
的中点
,连接
.
(1)【方法体会】线段
,
有着特别的关系,请依据思路将横线处补充完整.
解:在图甲中,将线段
延长至点
,使
,连接
,
,交
于点
.
则:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1e0c08b99addcc37e4176f5882e8f.png)
即:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9195d58eb86b8cfacc37f3782eec27a7.png)
在
和
中:
∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c20968b91619283dd0bf4810cd3086.png)
∴______(
)
∴
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81f683bfa5fb4f5d901503bfa7ccf26.png)
设
,
交于点
,
又∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655be1d2908b97ed4df568a10177013.png)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6d4df1654d5d59864a7d4fd3bd27dd.png)
∴
,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
又∵点
是
中点,点
是
中点
∴
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14985aca12e83ce0d6400b65857c9a0.png)
又∵
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
∴
,
的位置关系是
_____;数量关系是______.
(2)【探索发现】如图乙,
交
于点
,交
于点
,交
于点
,当点
与点
重合时,求
:
的值;
(3)【拓展运用】若正方形的边长为
,连接
,
,在点
运动的过程中,当
时,请在备用图中画出此时的图形,并求出此时
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862730f28c12750ebea0af5edcac5fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/5a5fa1b3-5fba-4355-8120-99cda6f5fdce.png?resizew=509)
(1)【方法体会】线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
解:在图甲中,将线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faee0268e5ede6318697e5a8509dd6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c579436ff500a36fe7976012bc227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b62dc033d86ee9e561b8903796701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
则:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1e0c08b99addcc37e4176f5882e8f.png)
即:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9195d58eb86b8cfacc37f3782eec27a7.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c20968b91619283dd0bf4810cd3086.png)
∴______(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d7d84e698f6d38fa2be14d36c04988.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343f75b2c5479c279abca2faed278901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81f683bfa5fb4f5d901503bfa7ccf26.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/22/06ea4ec9-979b-4a8e-b791-ecdd1567f6b0.png?resizew=236)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655be1d2908b97ed4df568a10177013.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6d4df1654d5d59864a7d4fd3bd27dd.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86129aef281bd7f5da10963e5164d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
又∵点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87448e09eaa816e50ae92d111d5ded6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe5747aaac225fd08ad9789789b3804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14985aca12e83ce0d6400b65857c9a0.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343f75b2c5479c279abca2faed278901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bff235ce9338aeef7f2b952079cbb0f.png)
(2)【探索发现】如图乙,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a36775168095280f72504478345bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f37d57768f163f56619e531b9541ab.png)
(3)【拓展运用】若正方形的边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f30cb81835298cb612a828f355060a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd63ce2206748eb84eb2bebf459e754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e323c08b18488d11bd8f3cd74efa971a.png)
您最近一年使用:0次
2024-03-22更新
|
106次组卷
|
2卷引用:2024年贵州省部分学校2024年初中一模试题
真题
6 . 如图,在四边形
中,对角线
与
相交于点O,记
的面积为
,
的面积为
.
(1)问题解决:如图①,若AB//CD,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3682afa5e3e71971c82d35c98a6146.png)
(2)探索推广:如图②,若
与
不平行,(1)中的结论是否成立?若成立,请证明;若不成立,请说明理由.
(3)拓展应用:如图③,在
上取一点E,使
,过点E作
交
于点F,点H为
的中点,
交
于点G,且
,若
,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)问题解决:如图①,若AB//CD,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3682afa5e3e71971c82d35c98a6146.png)
(2)探索推广:如图②,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)拓展应用:如图③,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb43a62f3bfd7666ab898bcb5efc1ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117878cbd8c00f2aabcdf62b487e2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d51083cf65d74e2856c9755c1ebaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af28f52ccef42710bfb647db4f2f0f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/2/1272add9-2a69-405f-801e-3e29e0f200d3.png?resizew=419)
您最近一年使用:0次
名校
7 .
中,
,
,点
为直线
上一动点
点
不与
,
重合
,以
为边在
右侧作菱形
,使
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/57c69b52-779e-4094-bfd7-a72723d6c0c2.png?resizew=463)
(1)观察猜想:如图
,当点
在线段
上时,
与
的位置关系为:______.
,
,
之间的数量关系为:______;
(2)数学思考:如图
,当点
在线段
的延长线上时,结论
,
是否仍然成立?若成立,请给予证明;若不成立,请你写出正确结论再给予证明.
(3)拓展延伸:如图
,当点
在线段
的延长线上时,设
与
相交于点
,若已知
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deb742445686d17a88e979c95dacca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/57c69b52-779e-4094-bfd7-a72723d6c0c2.png?resizew=463)
(1)观察猜想:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6c6e83c3df632e1e94fc8f0f529cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50987e5e387450c63da0d6e528e873fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(2)数学思考:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
(3)拓展延伸:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71622531dfa894f21b2da123d020d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
您最近一年使用:0次
2022-09-19更新
|
182次组卷
|
6卷引用:2023年贵州省铜仁市中考三模数学模拟试题
8 . 小杰同学在中考总复习时,遇到一个课本上的问题,温故知识后进行了操作推理与拓展应用.
(1)温故知识:如图①,在
中,一个正方形
的边
在
上,顶点P,N分别在
,
上,作
于点D,交
于点E,若
,
.求正方形
的边长;(用含a,h的代数式表示)
(2)操作推理:如何画出这个正方形
呢?
如图②,小杰画出了图①的
,然后又进行以下操作:先在
边上任取一点
,画正方形
,使点
,
在
边上,点
在
内,然后连接
,并延长交
于点N,作
于点M,
交
于点P,
于点Q,得到四边形
.证明:图②中的四边形
是正方形;
(3)拓展应用:在(2)的基础上,在线段
上截取
,连接
,
(如图③),当
时,请直接写出线段
的长.(用含a,h的代数式表示)
(1)温故知识:如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](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/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d22f065ec04de109d913e8e7855110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(2)操作推理:如何画出这个正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
如图②,小杰画出了图①的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca9581c221aa3016b035444015a7e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d486055c508b9ff7f79fb8d2a464458b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dacd0086635538bf42d08bfdaf481cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2c2bfe8c8337ca8f2fba6af5fddec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f24325565a9dd95128a633a240da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(3)拓展应用:在(2)的基础上,在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df7c43dd51ecde238a068b8138e8b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e33bc76f589215d9738bfc3988bfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2972987740037120/2979393519583232/STEM/a1756d1a-bd5b-4850-b603-4d3b2878a69f.png?resizew=570)
您最近一年使用:0次
9 . 数学实践活动,是一种非常有效的学习方式.通过活动可以激发我们学习兴趣,提高动手动脑能力,拓展思维空间,丰富数学体验.让我们一起动手来折一折、转一转、剪一剪,体会活动带来我们的乐趣.
折一折:将正方形纸片
折叠,发现
、
都落在对角线
上,展开得折痕
、
,连接
,如图1
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982793640869888/2984942321958912/STEM/4898928116df49668fe624691fba74b3.png?resizew=131)
(1)
______°,写出图中两个等腰三角形:_____(不需要添加字母);
(2)转一转:将图1中
绕点A旋转,使它的两边分别交边
、
于点
、
,连接
,如图2,线段
、
、
之间的数量关系为______;
(3)连接正方形对角线
,如图2中的
的边
、
分别交对角线
于点
、点
,如图3,则
______;
(4)剪一剪:将图3中的正方形纸片沿对角线
剪开,如图4.求证:
.
折一折:将正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982793640869888/2984942321958912/STEM/0e3b1549bdd34903ba634bd7d6a487b6.png?resizew=387)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982793640869888/2984942321958912/STEM/4898928116df49668fe624691fba74b3.png?resizew=131)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e569f82eb96d237501ed0fba536e9ac4.png)
(2)转一转:将图1中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e31edc5b71c488ca9942d70d9298f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
(3)连接正方形对角线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94874d85399fc67d9d86bbb89acadeca.png)
(4)剪一剪:将图3中的正方形纸片沿对角线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc386f4abe6ec5082f9507c91ddc16d.png)
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10 . 综合与实践:
数学实践活动,是一种非常有效的学习方式,通过活动可以激发我们的学习兴趣,提高动手动脑能力,拓展思维空间,丰富数学体验,让我们一起动手来折一折、转一转、剪一剪,体会活动带给我们的乐趣.
折一折:将正方形纸片ABCD折叠,使边AB,AD都落在对角线AC上,展开得折痕AE,AF,连接EF,如图①.
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936830962737152/2942326775701504/STEM/aba8afbd-c5c6-4a03-95f4-aa442823c60b.png?resizew=440)
(1)∠EAF=______°,写出图中两个等腰三角形:__________(不需要添加字母);
转一转:将图①中的∠EAF绕点A旋转,使它的两边分别交边BC,CD于点P,Q,连接PQ,如图②.
(2)判断线段BP,PQ,DQ之间的数量关系并证明;
(3)连接正方形对角线BD,若图②中的∠PAQ的边AP,AQ分别交对角线BD于点M,点N,如图③,求
的值.
数学实践活动,是一种非常有效的学习方式,通过活动可以激发我们的学习兴趣,提高动手动脑能力,拓展思维空间,丰富数学体验,让我们一起动手来折一折、转一转、剪一剪,体会活动带给我们的乐趣.
折一折:将正方形纸片ABCD折叠,使边AB,AD都落在对角线AC上,展开得折痕AE,AF,连接EF,如图①.
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936830962737152/2942326775701504/STEM/aba8afbd-c5c6-4a03-95f4-aa442823c60b.png?resizew=440)
(1)∠EAF=______°,写出图中两个等腰三角形:__________(不需要添加字母);
转一转:将图①中的∠EAF绕点A旋转,使它的两边分别交边BC,CD于点P,Q,连接PQ,如图②.
(2)判断线段BP,PQ,DQ之间的数量关系并证明;
(3)连接正方形对角线BD,若图②中的∠PAQ的边AP,AQ分别交对角线BD于点M,点N,如图③,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e53cf4715617576ddcaccce03b7969.png)
您最近一年使用:0次