如图1,矩形ABCD中,点E是边AD上动点,点F是边BC上动点,连接EF,把矩形ABCD沿直线EF折叠,点B恰好落在边AD上,记为点G;如图2,把矩形展开铺平,连接BE,FG.
![](https://img.xkw.com/dksih/QBM/2020/2/5/2392275688595456/2392566951247872/STEM/6aa62f73fe434bef82eca2f7cedbddcf.png?resizew=317)
(1)判断四边形BEGF的形状一定是 ,请证明你的结论;
(2)若矩形边AB=4,BC=8,直接写出四边形BEGF面积的最大值为 .
![](https://img.xkw.com/dksih/QBM/2020/2/5/2392275688595456/2392566951247872/STEM/6aa62f73fe434bef82eca2f7cedbddcf.png?resizew=317)
(1)判断四边形BEGF的形状一定是 ,请证明你的结论;
(2)若矩形边AB=4,BC=8,直接写出四边形BEGF面积的最大值为 .
18-19八年级下·北京东城·阶段练习 查看更多[2]
更新时间:2020-02-05 17:52:50
|
相似题推荐
解答题-问答题
|
适中
(0.65)
名校
【推荐1】如图,在矩形纸片
中,
,
,点E在
上,将
沿
折叠,使点A落在对角线
上的点
处,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b65065ec3a0cb4b050989165c003d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b43490ca09467a4c8cd8cfe91c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b10100be43f77a13fa0ccd1c1d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/c9c94304-f5af-4f30-abb7-c7ae0120d662.png?resizew=160)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐2】如图,在矩形ABCD中,AB=6,P为边CD上一点,把
沿直线BP折叠,顶点C折叠到
,连接
与AD交于点E,连接CE与BP交于点Q,若CE⊥BE.
(1)求证:
ABE ∽
DEC;
(2)当AD=13时,AE>DE,求CE的长;
(3)连接
,
①判断四边形
的形状.请说明理由.
②当CP=4时,并求CE•EQ的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(2)当AD=13时,AE>DE,求CE的长;
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702518d070e667c54087eebed9c410b7.png)
①判断四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7778d3e02de5c4cfaf4c663e8dca85.png)
②当CP=4时,并求CE•EQ的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/9cdbcc32-af60-498f-82ea-9e3fda27b33f.png?resizew=154)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
真题
【推荐1】在学习了矩形与菱形的相关知识后,小明同学进行了更深入的研究,他发现,过矩形的一条对角线的中点作这条对角线的垂线,与矩形两边相交的两点和这条对角线的两个端点构成的四边形是菱形,可利用证明三角形全等得到此结论.根据他的想法与思路,完成以下作图与填空:
中,点
是对角线
的中点.用尺规过点
作
的垂线,分别交
,
于点
,
,连接
,
.(不写作法,保留作图痕迹)
(2)已知:矩形
,点
,
分别在
,
上,
经过对角线
的中点
,且
.求证:四边形
是菱形.
证明:∵四边形
是矩形,
∴
.
∴①,
.
∵点
是
的中点,
∴②.
∴
(AAS).
∴③.
又∵
,
∴四边形
是平行四边形.
∵
,
∴四边形
是菱形.
进一步思考,如果四边形
是平行四边形呢?请你模仿题中表述,写出你猜想的结论:④.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/9d78abbad68bbbf12af10cd40ef4c353.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)已知:矩形
![](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/a0ed1ec316bc54c37c4286c208f55667.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4a54cc7818be87a239f6de5f5d05b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
证明:∵四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
∴①,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2914e8388901363fcd96bbf26c67103.png)
∵点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
∴②.
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3716146b2867fda6dbeb90aabf05b6.png)
∴③.
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a23f35ebcd9799d82c1e41c09781a4c.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4a54cc7818be87a239f6de5f5d05b.png)
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
进一步思考,如果四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在△ABC中,AB=AC,以AB为直径的圆O分别与BC,AC交于点D,E,点F在AC边上,DF是圆O的切线.
![](https://img.xkw.com/dksih/QBM/2022/2/19/2919955130400768/2921927309877248/STEM/89323fa7-156d-442e-ac18-6f8340359c90.png?resizew=172)
(1)证明:DF⊥AC;
(2)连接OD,DE,当AC=4FC时,判断四边形AODE的形状,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2022/2/19/2919955130400768/2921927309877248/STEM/89323fa7-156d-442e-ac18-6f8340359c90.png?resizew=172)
(1)证明:DF⊥AC;
(2)连接OD,DE,当AC=4FC时,判断四边形AODE的形状,并证明你的结论.
您最近一年使用:0次