2021年初中常用数学模型.pdf

.word.zl.【1】中点+平行模型如图，如果ABDE，且 C 为 AE 中点，那么有ABC EDC 很好证的，当然十 分实用，经常 需要添加辅助线例如延长【例 题1】2021 某 模 拟【例题2】2021 答案：1.32；2.D【2】一线三等角模型如图，假设 B=C=DEF=0 90)那么一定有 BDE 与 CEF相 似。十 分 好 证 外 角 和 什 么 一 大 堆 ，并 且 也 很 实 用。经 常 在 矩 形 里 出 题。|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 11 页.word.zl.【例题1】2021【例题2】2006【例题 3】原创答案：1.2或3-24或252.(5453-，)【3】巧造旋转模型在某些几何题中，往往有一些奇怪的结论，此时可以通过几何三大变换之 一【旋 转】求 解。巧 造 旋 转 往 往 要 有 一 定 的 等 量 关 系 和 特 殊 角 度，如 下 题：|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.通 过 观 察 可 得 ABC=C=45，AB=AC。我们可以将ACD 绕 A 顺时针旋转90得到 ABE，使得 AC与 AB 重合。那么就有EBBC，而在RT AED 中，DE2=2AD2等腰直角三角形所以BE2+BD2=DE2，即 BD2+CD2=2AD2是不是赶脚很难想到？要学会判断，这种感觉是要练出来的！【例题1】2021【例题 2】【例题 3】2021 改编|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.答案：1.412.9 3.(1.)2，(2.)直角三角形，旋转后证全等，证明略【4】等腰模型这是一个很根底的模型什么样的构造会生成等腰三角形首先：平行+角平分线，如图，假设 AD BE，BC 平分 ABE，那么 AB=AC，很好证的，导角即可。其次：垂直+角平分这个不难理解，因为等腰三角形三线合一。这种模型很常用，常常需要做辅助线延长之类【例题1】原创|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.ABCD【例题2】原创【例题3】改编1.11 2.3 3.延长 CD 交 AB 于 M，利用中位线，证明略【5】倍长中线法常考，选填大证明都可能会用。是的！又是中点，中点用的很多啊=这个模型怎么用？先要判断。做题的时候看见中点，先找有没有可以直接用的，没有就找就没有平行+中点，再没有就要想了没事摆个中点在这里有啥用？这时试试倍长中线。记住一 句 话：“倍 长 中 线，定 得 全 等 先 来 举 一 个 例 子，吧 里 很 经 典 的 一 题。_解：延长 AD，使DE=AD，连接 CE做这种题不变的辅助线说明AD=DE，BD=CD，ADB=CDE ADB EDC CE=AB=3 4-3AE4+3故 1/2AD7/2这样就迎刃而解了，还有好多好多题，需要用到这个【例题1】改编|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.【例题2】改编1.6 2.证明略，(3.)22【6】几何最值模型.1最值是中考最常考的题目，选择、填空、大题都可能有。几何最值当然数学书上是找不到的，所以这要我们平时多了解这种题的做题技巧一般有三种：线段最值、折线最值、周长面积最值最值不好学，先从简单学起。1.首先最简单的：点到直线的距离垂线段最短、化曲为直，这是最根底的。2.其次：通过对称寻找最值，经典的【建立奶站】模型。3.折叠最值：三角形三边关系解题，寻找【三点共线】最关键。举个例子：第一问做一个垂线就行了。第二问是重点，作C 关于 l 的对称点C，连接 CB，那么 CB 与 l 的交点为Q，此时BQ+CQ 最小值为BC。用三角形三边关系证明，尝试一下吧第三问同样重点虽然没第二问那么常考，M 可不是 AD 与 l 的交点，这时因为A、D 在异侧讨论差值不方便，故作对|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.称。那么AD 延长线与l 的交点为M，此时 lAM-DMl的最小值为DM。这同样用三角形三边关系证。考试的时候辅助线要写，道理不用。简单归纳，同侧最小找轴对称、异侧最大对称 加 延 长，注 意 图 形 对 称 性 好 了 先 到 这 里，下 面 是 例 题【例 题1】改 编【例题2】原创1.4 2.(1.)2-6；(2.)62；FABG、15为 BG 的垂直平分线与BC 的交点【7】几何最值模型.2初局部的几何最值都要化曲为直，一般我们称为【三点共线】，下面是折叠的一题。做这种题，最重要找的是不变量。如图，CD 是不变量6，AD 也是不变量61，只有 E、F在动现在开场分析，先把AD 连接，得到一个不变的线段。而在ADF 中，由三边公式可知 AFAD-DF，这有什么用？这个意思是万一A、F、D 三点共线 了，不就是AF=AD-DF了？就是说当形成了三角形的时候，AF 都是大于AD-DF的，三点共线时，AF=AD-DF，这 样AF不 就 最 短 了 吗？所 以AFmin=61-6还 有 一 种 经 典 的 题：|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6.word.zl.照样先找不变量，发现AB、BC 不变为 4，其余没有。这种题的不变量一般隐藏在某些条件中分析一下：等边你还没用，AOB=90的条件也没用，综合考虑，取 AB 中点，因为直角三角形斜边中线等于斜边一半，所以OD=2，由等边三角形，可知CD=2 3，现在用三点共线，很快得到OC=OD+CD时 OC 最大，所以OC 最大值为2+23 这种题要多练，寻找 感 觉。主 要 是 找 不 变 量，这 在 动 点 问 题 中 十 分 重 要。【例 题1】【例题 2】呵呵你会发现我偷懒了|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 8 页，共 11 页文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2N5X4G7 ZG8N5O2K4R6文档编码:CT1I6K6P5C8 HO3A2