我们定义:如图1,在△ABC中,把AB点绕点A顺时针旋转
得到
.把AC绕点A逆时针旋转
得到
,连接
.当
=180°时,我们称△
是△ABC的“旋补三角形”,△A
边
上的中线AD叫做△ABC的“旋补中线”,点A叫做“旋补中心”.
特例感知:
(1) 在图2,图3中,△A
是△ABC的“旋补三角形”,AD是△ABC的“旋补中线”
① 如图2,当△ABC为等边三角形时,AD与BC的数量关系为AD= BC.
②如图3.当∠BAC=90°,BC=8时,则AD长为
[猜想论证]
(2) 在图1中,当△ABC为任意三角形时,猜想AD与BC的数量关系,并给予证明.
[拓展应用]
(3) 如图4,在四边形ABCD内部恰好存在一点P,使△PDC是△PAB的“能补三角形”,自行补图形,∠C=90°,∠D=150°,BC=12,CD=
,AB=2
.直接写出△PAB的“旋补中线”长是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36471e4e7749cd8da4bc9b4b3dc85fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ac8c5700ce2de9a140c4adea742168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecbed9cb44cd1f0bad05d3db2ffff18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d59152f6b55e50dffbc6e9cda21fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
特例感知:
(1) 在图2,图3中,△A
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
① 如图2,当△ABC为等边三角形时,AD与BC的数量关系为AD= BC.
②如图3.当∠BAC=90°,BC=8时,则AD长为
[猜想论证]
(2) 在图1中,当△ABC为任意三角形时,猜想AD与BC的数量关系,并给予证明.
[拓展应用]
(3) 如图4,在四边形ABCD内部恰好存在一点P,使△PDC是△PAB的“能补三角形”,自行补图形,∠C=90°,∠D=150°,BC=12,CD=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985f75c624e091eca4809b1dd94f0530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766dfef2a4159f49c7bd349fb36d670.png)
![](https://img.xkw.com/dksih/QBM/2020/10/26/2579559719550976/2580738071461888/STEM/a89e26e3602241828651e14976d57b55.png?resizew=479)
更新时间:2020-10-28 14:27:57
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解答题-作图题
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【推荐1】如图是边长为个
单位长度的小正方形组成的
网格,每个小正方形的顶点叫做格点.图中
、
、
都是格点,点
是线段
的延长线与横格线的交点.仅用无刻度的直尺在给定的网格中画图(画图结果用实线,画图过程用虚线).
(1)把线段
向右平移
个单位长度得到线段
,画出线段
;
(2)在
上找一点H,使
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(3)作点
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为平行四边形,在
上作点
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(1)把线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
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(3)作点
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9186e4574ffe28e673724fcb019db208.png)
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解答题-证明题
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【推荐2】如图.
,点O在
上,
与
相切于点A,与
的交点分别为B,C.作
,与
交于点D,作
,垂足为E,连接
并延长,交
于点F.
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(1)求证:
;
(2)若
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的长.
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(1)求证:
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(2)若
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解答题-证明题
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【推荐1】如图所示,
和
是等腰直角三角形,
,点
、
在
的外部,连结
,
.
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(1)求证:
;
(2)若将
绕点
旋转,直线
交直线
于点
,交直线
于点
.
①如果
,
,求
的值;
②当
为等腰直角三角形时,请你直接写出
的值.
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(1)求证:
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(2)若将
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①如果
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②当
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解答题-问答题
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名校
【推荐2】平面直角坐标系中,过点M
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(1)求经过A、N、B三点的抛物线的解析式.
(2)如图①,点E为(1)中抛物线的顶点,连接EN,判断直线EN与⊙O的位置关系,并说明理由.
(3)如图②,连接MD、BD,过点D的直线
交抛物线于点P,且
,直接写出直线DP的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dccc5720967ee3edce0174255e8ed8.png)
(1)求经过A、N、B三点的抛物线的解析式.
(2)如图①,点E为(1)中抛物线的顶点,连接EN,判断直线EN与⊙O的位置关系,并说明理由.
(3)如图②,连接MD、BD,过点D的直线
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