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风筝形四边形与向量构造演示

风筝形四边形与向量构造演示
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2016-03-14 05:30
多边形向量解析几何几何作图
①本范例演示了如何利用GeoGebra构造一个风筝形（kite）四边形，并展示其几何特征与相关向量关系。②核心数学概念包括风筝形四边形的定义（两组相邻边相等）、对角线性质（一条对角线垂直平分另一条）、以及二维向量的表示与运算。③作图要点：从构造摘要看，使用了Segment命令绘制各边，并通过AttachCopyToView将文本对象固定到视图，涉及点A、B、C、D，线段a、b、c、d、e、f以及stroke1、stroke2等对象，可能用于标注或辅助线。④适合中学几何教学，用于直观理解特殊四边形的性质，也可作为向量入门示例，帮助学生将几何图形与代数向量联系起来。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Segment(C, D) → c
  4. Segment(B, D) → d
  5. Segment(A, D) → e
  6. Segment(B, C) → f
  7. AttachCopyToView(PolyLine[(3.0554146970381177, 0.9509390578620286), (3.1533174763549736, 0.9509390578620286), (3.270800811535201, 0.9509390578620286), (3.3491230349886862, 0.9509390578620286), (3.3491230349886862, 0.8726168344085439), (3.3491230349886862, 0.7942946109550593), (3.3491230349886862, 0.6768112757748322), (3.3491230349886862, 0.5984890523213475), (NaN, NaN), (2.7029646914974355, 0.5984890523213475), (2.7029646914974355, 0.4614251612777494), (2.7029646914974355, 0.38310293782426474), (2.7029646914974355, 0.3047807143707801), (2.7029646914974355, 0.1872973791905531), (2.7029646914974355, 0.10897515573706844), (2.7617063590875492, 0.14813626746381076), (2.8400285825410343, 0.1872973791905531), (2.918350805994519, 0.1872973791905531), (NaN, NaN), (2.9575119177212614, 1.1663251723591115), (2.8008674708142918, 1.1663251723591115), (2.7029646914974355, 1.1467446164957402), (2.6833841356340646, 1.0684223930422556), (2.6833841356340646, 0.9509390578620286), (2.7029646914974355, 0.892197390271915), (2.7029646914974355, 0.8138751668184304), (2.7225452473608067, 0.7159723875015745), (2.7225452473608067, 0.6376501640480899), (NaN, NaN), (3.3491230349886862, 0.5201668288678629), (3.3491230349886862, 0.4222640495510071), (3.3491230349886862, 0.32436127023415123), (3.3491230349886862, 0.2460390467806666), (3.3491230349886862, 0.16771682332718194), (3.25122025567183, 0.16771682332718194), (3.1533174763549736, 0.16771682332718194), (3.0358341411747465, 0.16771682332718194), true], 1, (-3.77819929927844, -4.8449054776958365), (20.87372053270593, 6.081044694065274), (0, 558), (1259, 0)) → stroke1
  8. AttachCopyToView(PolyLine[(2.800867470814292, 2.262836300707897), (2.8400285825410347, 2.164933521391041), (2.8791896942677773, 2.086611297937556), (2.977092473584633, 2.047450186210814), (3.0749952529014895, 2.0278696303474426), (3.1533174763549745, 2.0082890744840713), (3.231639699808459, 2.0082890744840713), (3.290381367398573, 2.0278696303474426), (3.3491230349886867, 2.067030742074185), (3.4078647025788005, 2.1257724096642985), (NaN, NaN), (2.7617063590875497, -1.8882415423267904), (2.8400285825410347, -1.8686609864634194), (2.91835080599452, -1.829499874736677), (2.977092473584633, -1.7903387630099346), (3.0749952529014895, -1.7707582071465635), (3.1337369204916032, -1.7511776512831922), (3.212059143945088, -1.7511776512831922), (3.2708008115352016, -1.8099193188733058), (3.3295424791253154, -1.8490804306000481), (3.3491230349886867, -1.946983209916904), (3.3295424791253154, -2.025305433370389), true], 1, (-3.7781992992784397, -4.8449054776958365), (20.87372053270593, 6.081044694065274), (0, 558), (1259, 0)) → stroke2