2022年2015中考试题研究数学精品复习专题跟踪突破二开放探究型问题 .pdf

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1、专题跟踪突破二开放探究型问题一、选择题(每小题 6 分，共 30 分)1(2013贵阳)如图，M 是 Rt ABC 的斜边 BC 上异于 B，C 的一定点，过 M 点作直线截 ABC，使截得的三角形与ABC 相似，这样的直线共有(C)A1 条B2 条C3 条D 4 条2(2014荆门)如图，在 44 的正方形网格中，每个小正方形的顶点称为格点，左上角阴影部分是一个以格点为顶点的正方形(简称格点正方形)若再作一个格点正方形，并涂上阴影，使这两个格点正方形无重叠面积，且组成的图形是轴对称图形，又是中心对称图形，则这个格点正方形的作法共有(C)A2 种B3 种C 4 种D5 种3(2013龙岩)如图

2、，在平面直角坐标系xOy 中，A(0，2)，B(0，6)，动点 C 在直线 yx 上若以A，B，C 三点为顶点的三角形是等腰三角形，则点 C 的个数有(B)A2 个B3 个C 4 个D5 个4(2014玉林)蜂巢的构造非常美丽、科学，如图是由7 个形状、大小完全相同的正六边形组成的网络，正六边形的顶点称为格点，ABC 的顶点都在格点上设定AB 边如图所示，则 ABC 是直角三角形的个数有(C)A4 个B6 个C 8 个D10 个文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档

3、编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y

4、2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9

5、 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7

6、文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L

7、2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7

8、J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1

9、Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y75(2014资阳)二次函数yax2bxc(a 0)的图象如图，给出下列四个结论：4acb20；4a c2b；3b2c0；m(am b)ba(m 1)，其中正确的个数是(B)A4 B3 C2 D1 二、填空题(每小题 6 分，共 30 分)6(2014温州)请举反例说明命题“对于任意实数x，x25x5 的值总是整数”是假命题，你举的反例是x_12_(写出一个x 的值即可)7(2014吉林)如图，OB 是 O 的半径，弦 AB OB

10、，直径 CDAB，若点 P 是线段OD 上的动点，连接PA，则 PAB 的度数可以是 _65 度(60 度 A75 度，答案不唯一)_(写出一个即可),第 7 题图)文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7

11、L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K

12、7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L

13、1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6

14、P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W

15、2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V

16、5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7,第 8 题图)8(2014 娄底)如图，要使平行四边形ABCD 是矩形，则应添加的条件是_ABC

17、 90或 ACBD(答案不唯一)_(添加一个条件即可)9(2014赤峰)直线l 过点M(2，0)，该直线的解析式可以写为_yx2(答案不唯一)_(只写出一个即可)10(2013 昭通)如图，AB 是 O 的直径，弦 BC4 cm，F 是弦 BC 的中点，ABC 60.若动点E 以 1 cm/s 的速度从A 点出发在AB 上沿着ABA 运动，设运动时间为t(s)(0t16)，连接 EF，当 BEF 是直角三角形时，t 的值为 _4 或 7 或 9 或 12_(填出一个正确的即可)三、解答题(共 40 分)11(8 分)(2013 云南)如图，点 B 在 AE 上，点 D 在 AC 上，AB AD

18、.请你添加一个适当的条件，使 ABC ADE.(只能添加一个)(1)你添加的条件是_C E(或 ABC ADE 或 EBC CDE 或 AC AE 或 BEDC)_；(2)添加条件后，请说明 ABC ADE 的理由文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9

19、ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文

20、档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2

21、Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J

22、9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y

23、7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7

24、L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7解：(1)AB AD，A A，若利用“AAS”，可

25、以添加 C E，若利用“ASA”，可以添加 ABC ADE，或 EBC CDE，若利用“SAS”，可以添加AC AE，或 BEDC，综上所述，可以添加的条件为C E(或 ABC ADE 或 EBC CDE 或 ACAE 或 BEDC)(2)选 C E 为条件理由如下：在 ABC 和 ADE 中，A A，C E，AB AD，ABC ADE(AAS)12(8 分)(2012 吉林)在如图所示的三个函数图象中，有两个函数图象能近似地刻画如下 a，b 两个情境：情境 a：小芳离开家不久，发现把作业本忘在家里，于是返回了家里找到了作业本再去学校；情境 b：小芳从家出发，走了一段路程后，为了赶时间，以更快

26、的速度前进(1)情境 a，b 所对应的函数图象分别是_，_；(填写序号)(2)请你为剩下的函数图象写出一个适合的情境解：(2)情境是小芳离开家到公园，休息了一会儿，又走回了家文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3

27、P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O

28、1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M1

29、0V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:C

30、Q3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM

31、1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5

32、M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y713(12 分)(2013遵义)如图，在 RtABC 中，C90，AC 4 cm，BC3

33、cm.动点M，N 从点 C 同时出发，均以每秒1 cm 的速度分别沿CA，CB 向终点 A，B 移动，同时动点 P 从点 B 出发，以每秒 2 cm 的速度沿BA 向终点 A 移动，连接 PM，PN，设移动时间为t(单位：秒，0t2.5)(1)当 t 为何值时，以 A，P，M 为顶点的三角形与ABC 相似？(2)是否存在某一时刻t，使四边形APNC 的面积 S有最小值？若存在，求 S的最小值；若不存在，请说明理由解：如图，在 RtABC 中，C90，AC 4 cm，BC3 cm.根据勾股定理，得ABAC2BC25 cm.(1)以 A，P，M 为顶点的三角形与ABC 相似，分两种情况：当AMP

34、ABC 时，APACAMAB，即52t44 t5，解得 t32当 APM ABC 时，AMACAPAB，即4 t452t5，解得t0(不合题意，舍去)；综上所述，当 t32时，以 A，P，M 为顶点的三角形与ABC 相似(2)存在某一时刻t，使四边形APNC 的面积 S 有最小值 理由如下：假设存在某一时刻t，使四边形 APNC 的面积 S有最小值 如图，过点 P 作 PHBC 于点 H.则 PHAC，PHAC文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P

35、7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2

36、K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5

37、L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P

38、6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1

39、W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10

40、V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ

41、3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7BPBA，即PH42t5，PH85t，SSABCSBPN123412(3 t)85t45(t32)2215(0t2.5)450，S 有最小值当t32时，S最小值21514(12 分)(2014 东营)【探究发现】如图，ABC是等边三角形，AEF60，EF 交等边三角形外角平分线CF 所在的直线于点F，当点 E 是 BC 的中点时，有 AEEF 成立；【数学思考】某数学兴趣小组在探究AE，EF 的关系时，运用“从特殊到一般”的数学思想，通过验证得出

42、如下结论：当点 E 是直线 BC 上(B，C 除外)任意一点时(其他条件不变)，结论 AEEF 仍然成立假如你是该兴趣小组中的一员，请你从“点E 是线段 BC 上的任意一点”；“点E 是线段 BC 延长线上的任意一点”；“点 E 是线段 BC 反向延长线上的任意一点”三种情况中，任选一种情况，在图中画出图形，并证明 AEEF.【拓展应用】当点E 在线段 BC 的延长线上时，若 CE BC，在图中画出图形，并运用上述结论求出SABC SAEF的值解：证明：如图，“点 E 是线段 BC 上任意一点”时，在 AB 上截取 AG，使 AG EC，连接 EG，ABC 是等边三角形，ABBC，B ACB

43、60.AGEC，BGBE，BEG 是等边三角形，BGE60，AGE120.FC 是外角的平分线，ECF 120 AGE.AEC是 ABE的外角，AEC B GAE 60GAE.AEC AEF FEC60 FEC，GAE FEC.在 AGE 和 ECF中 GAE CEF，AG EC，AGE ECF，AGE ECF(ASA)，AEEF 文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6

44、P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W

45、2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V

46、5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3

47、P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O

48、1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M1

49、0V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:C

50、Q3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7拓展应用：如图：作CHAE 于 H 点，AHC 90.由数学思考得AEEF，又 AEF 60，AEF 是等边三角形，ABC AEF.CEBCAC，ABC 是等边三角形，CAH 30，AH EH.CH12AC，AH 32AC，AE3AC，ACAE33.SABCSAEF(ACAE)2(33)213文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V5L1Y7文档编码:CQ3P6P7L2Y2 HM1O1W2K7J9 ZZ5M10V