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对应角定理的逆定理：同位角相等则两直线平行

对应角定理的逆定理：同位角相等则两直线平行
几何画板及绘图内容加载中，请稍等……
2015-09-30 10:06
角解析几何几何作图
所属专题 Logic and Parallel Lines
本范例演示两条直线被第三条截线所截时，通过标记同位角并验证其相等，从而说明对应角定理的逆定理：若同位角相等，则两直线平行。核心概念包括平行线、截线、同位角、角相等与几何推理。作图使用 GeoGebra 的 Segment 命令绘制线段/直线，AttachCopyToView 将视图或对象副本固定到界面，并借助点 A、B、C、D、E、F、G、H、I、J、Q 与 stroke1、stroke2 构建角标记，text1 至 text23 标注条件、结论和说明。适合初中几何、平行线判定教学、GeoGebra 几何作图演示与课堂互动。

GeoGebra 命令及参数

  1. AttachCopyToView(PolyLine[(1.9000000000000001, 4.259999999999999), (1.98, 4.259999999999999), (2.06, 4.259999999999999), (2.12, 4.279999999999999), (2.2, 4.279999999999999), (NaN, NaN), (2.48, 4.259999999999999), (2.56, 4.279999999999999), (2.64, 4.279999999999999), (2.7, 4.299999999999999), (2.7800000000000002, 4.299999999999999), true], 1, (-4.3, -5.239999999999997), (22.8, 6.299999999999998), (-220.99999999999991, 595), (1134, 18.00000000000011)) → stroke1
  2. Segment(C, D) → b
  3. Segment(E, F) → Q
  4. Segment(A, B) → a
  5. Segment(G, H) → c
  6. Segment(I, J) → d
  7. AttachCopyToView(PolyLine[(-3.0599999999999996, -1.519999999999998), (-2.9999999999999996, -1.4799999999999982), (-2.9399999999999995, -1.4599999999999982), (-2.8599999999999994, -1.4599999999999982), (-2.7999999999999994, -1.4399999999999982), (-2.7399999999999998, -1.4199999999999982), (-2.6599999999999997, -1.4199999999999982), (-2.5799999999999996, -1.4199999999999982), (NaN, NaN), (-2.2399999999999998, -1.4799999999999982), (-2.1799999999999997, -1.4999999999999982), (-2.0999999999999996, -1.4999999999999982), (-2.0199999999999996, -1.4999999999999982), (-1.9399999999999997, -1.4999999999999982), (-1.8599999999999997, -1.4999999999999982), (-1.7799999999999998, -1.4999999999999982), true], 1, (-3.9999999999999996, -5.279999999999996), (23.099999999999998, 6.259999999999998), (0, 577), (1355, 0)) → stroke2

AI 绘图提示语参考

画两条平行线被一条横线截断的图形。首先画两条平行线 a 和 b，然后画一条横线 c 与 a 和 b 相交，形成四个角。接着画另一条横线 d 与 a 和 b 相交，形成另外四个角。确保 c 和 d 与 a 和 b 形成的角相等，以展示对应的角相等意味着两条线平行。
以上提示语为根据原始绘图命令整理而来，仅供参考。