三个等角的顶点在同一条直线上,称一线三等角模型(角度有锐角、直角、钝角,若为直角,则又称一线三垂直模型).解决此模型问题的一般方法是利用三等角关系找全等或相似三角形所需角的相等条件,利用全等或相似三角形解决问题.
如图1,在四边形
中,点
为
上一点,
,求证:
.
【思考探究】
(2)如图2,在四边形
中,点
为
上一点,当
时,上述结论是否依然成立?说明理由.
【拓展延伸】
(3)请利用(1)(2)获得的经验解决问题:
如图3,在
中,
,
,以点
为直角顶点作等腰
,点
在
上,点
在
上,点
在
上,且
,若
,求
的长.
如图1,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7502d2b89b731a7c11faa97815d46d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c4bc1c164e8dd6747cf998b237ef90.png)
【思考探究】
(2)如图2,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500244f771b0e34b7fd1970e6757e5d5.png)
【拓展延伸】
(3)请利用(1)(2)获得的经验解决问题:
如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099026716ee1821dd7d9f157dc055f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e7ba6e267dde1a65a98f9f36b585ce.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02a4bbef957f179f55c28b37c64ce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4307209e1e5cad88fc1b8163858688ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
23-24九年级上·广西柳州·阶段练习 查看更多[2]
更新时间:2024-03-12 08:32:02
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相似题推荐
解答题-证明题
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适中
(0.65)
【推荐2】已知AD和BE相交于点C,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/413d4469-cc52-4be5-b4fc-24fd45d94622.png?resizew=425)
(1)如图(1),求证:
;
(2)如图(2),点P是线段BC上一点,连结AP.
①求证:
;
②若
,请直接写出
的度数;
(3)如图(3),若点M是射线BA上一点,作
直线AD于点H,
与
的角平分线相交于点N,请直接写出
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69de3884471034219ce4405544cdbb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94b028894e34a763f7d75a6f5a6132e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/413d4469-cc52-4be5-b4fc-24fd45d94622.png?resizew=425)
(1)如图(1),求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd81adb13f5a7550b0f94f770900a613.png)
(2)如图(2),点P是线段BC上一点,连结AP.
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6897cf1c11724c94b4d1508659254e.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17051a9531a9e677799c04c5dcbae614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a71e8a816d9ef65d4bffd81fd53216.png)
(3)如图(3),若点M是射线BA上一点,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a984e08781547575be9680e8c61bb21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dc2d2dd56fcc67698c45a6e0e48f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d76d1f1c2cccdc00e111e4f37b74459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629a687148b89998209cb70bb1bd089a.png)
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名校
【推荐1】如图,四边形ABCD是⊙O的内接四边形,∠ABC=90°,AD=CD,过A作⊙O的切线交CD的延长线于点P.
(2)若AB=6,BC=8,求PA、PD的长.
(2)若AB=6,BC=8,求PA、PD的长.
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解答题-证明题
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名校
【推荐2】如图,
是
的外接圆,
,
于点
,
延长线交
于点
.
;
(2)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.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/b9100c20868e5e6f3c2c1219abf36a47.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cbfaec1d9dcaaf159b060163436113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
您最近一年使用:0次
解答题-证明题
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适中
(0.65)
【推荐1】如图,在四边形
中,
,
,垂足为O,过点D作
的垂线交
的延长线于点E.
(1)求证:四边形
是平行四边形;
(2)若
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/6/c870d331-5b41-4d85-a546-31dbec099124.jpg?resizew=177)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9beeedb7ddaac2cd3d37151d058ab7fb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4dfbbe8b218b1b505df9117ccebd08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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【推荐2】已知:如图,直线y=x﹣15与x轴、y轴分别相交于点A和点B.抛物线
经过A、B两点.
![](https://img.xkw.com/dksih/QBM/2019/12/17/2356930661670912/2357971840720896/STEM/b1722e2d1ba0439ca763f2ba23a8a28b.png?resizew=154)
(1)求这个抛物线的解析式;
(2)若这抛物线的顶点为点D,与x轴的另一个交点为点C.对称轴与x轴交于点H,求△DAC的面积;
(3)若点E是线段AD的中点.CE与DH交于点G,点P在y轴的正半轴上,△POH是否能够与△CGH相似?如果能,请求出点P的坐标;如果不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90731f6d4190300b33385ce70eb2783a.png)
![](https://img.xkw.com/dksih/QBM/2019/12/17/2356930661670912/2357971840720896/STEM/b1722e2d1ba0439ca763f2ba23a8a28b.png?resizew=154)
(1)求这个抛物线的解析式;
(2)若这抛物线的顶点为点D,与x轴的另一个交点为点C.对称轴与x轴交于点H,求△DAC的面积;
(3)若点E是线段AD的中点.CE与DH交于点G,点P在y轴的正半轴上,△POH是否能够与△CGH相似?如果能,请求出点P的坐标;如果不能,请说明理由.
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