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探究垂直线

探究垂直线
几何画板及绘图内容加载中，请稍等……
2019-03-07 21:34
解析几何几何作图
①本范例演示如何通过 GeoGebra 探究两条直线垂直的条件与性质；②涉及的核心数学概念包括直线方程、斜率、勾股定理、角度计算；③作图要点提炼自构造摘要，使用了 Element, Polygon, PointIn, Line, OrthogonalLine, Slope, LaTeX, Text, Angle 等命令与对象；④适合高中数学学生或教师用于理解垂直线判定与相关几何性质。

GeoGebra 命令及参数

  1. Element({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}, m) → actualM
  2. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  3. PointIn(viewBox) → A
  4. PointIn(viewBox) → B
  5. Line(A, baseLine) → line1
  6. OrthogonalLine(B, baseLine) → line2
  7. Slope(line1) → slope1
  8. LaTeX("\text{Tilt}") → tilt
  9. LaTeX("\textbf{Instructions: }Lines 1 and 2 are perpendicular. Move the points and tilt the\\lines to investigate how they are related.") → INSTRUCTIONS
  10. LaTeX("\textbf{Question: }How are perpendicular lines related?") → QUESTION
  11. Slope(line2) → slope2
  12. Text("\textbf{Line \(1\)}", A + (-3.5, 0.5), true, true) → line1Label
  13. Text("\textbf{Line \(2\)}", B + (-3.5, 0.5), true, true) → line2Label
  14. Slope(line2) → slope2multiplier2
  15. Slope(line2) → slope2multiplier3
  16. Slope(line2) → slope2multiplier4
  17. Slope(line2) → slope2multiplier5
  18. Angle(line1, line2) → α