(1)计算:
.
(2)如图,在
中,D,E分别是
,
的中点,连接
并延长至点F,延长BC至点G,使得
,连接
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e056e3f333fd88c771edc1ae77262e6e.png)
(2)如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baedb038db26d9c599cdd2414695d772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb2f646f44a4e93cd5959b598eb57df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/524ccc17-5207-486f-8b4f-779850c7180b.png?resizew=166)
更新时间:2023-06-14 16:37:41
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相似题推荐
解答题-问答题
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【推荐1】如图,在平面直角坐标系中,已知
,
,
,a,b满足
,在第一象限内有一点D,已知
轴,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aeb7d8bfd4877a9bd85b7cc69aec40a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/24a35333-dd01-400d-b83e-ee75d2fe667e.png?resizew=392)
(1)求点D的坐标及四边形
的面积.
(2)在x轴上有一个动点P沿射线
的方向以每秒3个单位的速度从A点出发,经过t秒时有
的面积是
的面积的2倍,求t的值和对应P的坐标.
(3)在(2)的条件下,另有一动点M在射线
上运动,当点P、M运动到如图(2)的位置时有
,且
,作
平分
交
的延长线于H,请直接写出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c240561788bc63f41a6703219fb66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5612d598e27ac2ce0ab89fb63538bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541130d07517bebaee5f5577fe167023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c10ce68d3ee1dc8351a6c5a361bbaab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0122fba04c504636e801f962415f8a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aeb7d8bfd4877a9bd85b7cc69aec40a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/24a35333-dd01-400d-b83e-ee75d2fe667e.png?resizew=392)
(1)求点D的坐标及四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fdb48aaf0f4a2451390d27fb5f510a.png)
(2)在x轴上有一个动点P沿射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
(3)在(2)的条件下,另有一动点M在射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c04a48b5c5a4d65b7cd999c678d9161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd23ae4b8e7d4a60f38fc8e87fbc04e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b7d8c3ec6c616da49b61cd6e913f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe56082df0da2b6379113713522e3c29.png)
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解答题-证明题
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【推荐2】如图,四边形ABCD是平行四边形,E,F是对角线BD上的点,
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
(2)线段AF与CE有什么关系?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
(2)线段AF与CE有什么关系?请证明你的结论.
![](https://img.xkw.com/dksih/QBM/2021/6/25/2750564468998144/2768475400019968/STEM/80d368a0-d9fa-4205-a640-6a74be5dd13b.png?resizew=219)
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真题
【推荐1】已知△ABC中,M为BC的中点,直线m绕点A旋转,过B、M、C分别作BD⊥m于D,ME⊥m于E,CF⊥m于F.
(1)当直线m经过B点时,如图1,易证EM=
CF.(不需证明)
(2)当直线m不经过B点,旋转到如图2、图3的位置时,线段BD、ME、CF之间有怎样的数量关系?请直接写出你的猜想,并选择一种情况加以证明.
(1)当直线m经过B点时,如图1,易证EM=
![](https://img.xkw.com/dksih/QBM/2014/9/26/1573750726336512/1573750732734464/STEM/5b08aee9464043b195544559492c8675.png)
(2)当直线m不经过B点,旋转到如图2、图3的位置时,线段BD、ME、CF之间有怎样的数量关系?请直接写出你的猜想,并选择一种情况加以证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/2/d6a2b3ba-9c83-44ad-8a35-8c1031b256e9.png?resizew=505)
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【推荐2】如图,在四边形
中,
与
不平行,
,
分别是
,
的中点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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【推荐3】【综合与实践】
【探究】(1)小学我们就学过同底等高的两个三角形的面积相等,后来我们又学到等高的两个三角形的面积之比等于与高对应的底边长之比,如图(1),
的高
和
的高
相等,则
同样,同底的两个三角形,如果面积相等,也有类似的结论,若图形位置特殊,由此会产生一些新的结论,下面是小江同学探索的一个结论,请帮助小江完成证明.
和
的面积相等,求证:
.
证明:分别过点
、点
作
和
底边
上的高线
,
.
【应用】(2)把图(3)的四边形
改成一个以
为一边的三角形,并保持面积不变,请画出图形,并简要说明理由.
【拓展】(3)用上述探究的结论和已经证明的结论,证明三角形的中位线定理.
已知:如图(4),______.
求证:______.
证明:
【探究】(1)小学我们就学过同底等高的两个三角形的面积相等,后来我们又学到等高的两个三角形的面积之比等于与高对应的底边长之比,如图(1),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301941880d65680d8133f05b2785ce64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f0dadf037efedc90b39c57a6880a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
证明:分别过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f0dadf037efedc90b39c57a6880a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
【应用】(2)把图(3)的四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
【拓展】(3)用上述探究的结论和已经证明的结论,证明三角形的中位线定理.
已知:如图(4),______.
求证:______.
证明:
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