构造四分之三角的 GeoGebra 示例
几何画板及绘图内容加载中,请稍等……
①本范例演示如何使用 GeoGebra 构造一个角,其度数是已知角 ∠S 的四分之三;②涉及的核心数学概念包括角度测量、几何作图、比例关系;③作图要点——从下方『构造摘要』提炼用到了 Polygon(多边形)、Segment(线段)、Ray(射线)、Circle(圆)、Intersect(交点)、Midpoint(中点)、Vector(向量)、Translate(平移)、CircumcircleArc(圆弧)、Mirror(镜像)等 GeoGebra 命令/对象;④适合高中学段学生学习和理解角度比例关系及几何作图技巧。
GeoGebra 命令及参数
Polygon((22, y(Corner[1])), Corner[2], Corner[3], (22, y(Corner[4]))) → mask, a, b, c, dSegment(S, U) → FirstArcDistanceRay(S, U) → FirstAngleRay1Ray(S, FirstAngleRaypt) → FirstAngleRay2Circle(S, Segment[S, U]) → CircRad1Circle(S, (2 * Segment[S, U])) → CircRad2Intersect(CircRad2, FirstAngleRay1) → Udouble,Intersect(CircRad2, FirstAngleRay2) → Tdouble,Intersect(CircRad1, FirstAngleRay2) → T,Circle(U, Udouble) → CircCenUCircle(T, Tdouble) → CircCenTMidpoint(U, T) → FRay(S, F) → MidRayVector(S, S + (2 * (F - S))) → ShiftVecTranslate(F, ShiftVec) → FtranslatedIntersect(CircCenT, Segment[F, Ftranslated]) → W,CircumcircleArc(Tdouble, W, S) → ArcTCircumcircleArc(Udouble, W, S) → ArcUIntersect(CircRad2, MidRay) → A,Intersect(CircRad1, MidRay) → X,Midpoint(X, U) → GRay(S, G) → ThreeQuarterRayTranslate(G, Vector[(2 * Vector[S, G])]) → GtranslatedIntersect(ArcU, Segment[G, Gtranslated]) → Z,CircumcircleArc(A, Z, S) → ArcXMirror(X, FirstAngleRay1) → FirstArcAMirror(X, FirstAngleRay2) → FirstArcBCircumcircleArc(FirstArcB, X, FirstArcA) → FirstArcIntersect(ArcX, Segment[U, Udouble]) → B,CircumcircleArc(A, Z, B) → ArcXShortMidpoint(T, X) → CRay(S, C) → QuarterRayIntersect(ArcT, Segment[G, Gtranslated]) → I,CircumcircleArc(Tdouble, W, I) → ArcTShortTranslate(C, Vector[(2 * Vector[S, C])]) → CtranslatedIntersect(ArcU, Segment[C, Ctranslated]) → E,CircumcircleArc(Udouble, W, E) → ArcUShortRay(S, G) → EndRay1Ray(S, FirstAngleRaypt) → EndRay2
AI 绘图提示语参考
构造一个角,使其大小为给定角∠S的3/4。首先,画出角∠S的两条边,然后构造一个圆心在角顶点S,半径为角S边长两倍的圆,找到该圆与角两边的交点。接着,通过这些交点构造新的圆弧和射线,逐步调整角度直至达到3/4倍。最后,利用镜像和平移等操作,精确地确定出目标角的边。
以上提示语为根据原始绘图命令整理而来,仅供参考。