角平分线构造
几何画板及绘图内容加载中,请稍等……
①本范例演示了角平分线的几何构造方法;②涉及核心数学概念包括角、线段、圆、交点、向量等;③构造过程中用到了Angle, Segment, Point, Circle, Intersect, CircleArc, Ray, OrthogonalLine, Vector, Translate等GeoGebra命令;④适合初中及以上学生学习几何作图和角平分线性质。
GeoGebra 命令及参数
Angle(A_1, O, C_1) → αSegment(A_1, O) → aSegment(O, C_1) → bPoint(b) → ACircle(O, A) → cIntersect(c, a, 1) → BCircleArc(O, B, A) → dCircle(B, A) → eCircle(A, B) → fIntersect(f, e) → C, F, ,Ray(O, C) → gCircle(C, 0.6) → hIntersect(f, h) → G, H, ,Intersect(h, e) → I, J, ,CircleArc(B, I, A) → kCircleArc(A, B, G) → pPoint(g) → POrthogonalLine(P, b) → iOrthogonalLine(P, a) → jIntersect(b, i) → DIntersect(j, a) → ESegment(D, P) → lSegment(E, P) → mCircle(D, 0.7) → qCircle(E, 0.7) → rIntersect(q, b) → K, LIntersect(r, a) → M, NIntersect(r, m) → O_1,Intersect(q, l) → Q,Angle(M, E, O_1) → βAngle(Q, D, L) → γVector(A, B) → uTranslate(A, Vector[(u * n)]) → B'Ray(O, B') → sIntersect(d, s) → R,CircleArc(O, R, A) → tVector(A, I) → vTranslate(A, Vector[(v * (n - 1))]) → B'_1Ray(B, B'_1) → a_1Intersect(k, a_1) → S,CircleArc(B, S, A) → c_1Vector(G, B) → wTranslate(G, Vector[(w * (n - 2))]) → G'Ray(O, G') → b_1Intersect(p, b_1) → T,CircleArc(A, T, G) → d_1Circle(P, 2) → e_1Point(g) → UVector(O, U) → zTranslate(O, Vector[(z * (n - 3))]) → V'Segment(O, V') → f_1
AI 绘图提示语参考
画一个角的角平分线,先画出角的两条边和顶点,以顶点为圆心画一个圆与两边相交,连接交点和顶点,再以交点为圆心画两个圆,找到它们的交点,连接顶点和交点形成角平分线,最后以交点为圆心画圆,找到与角平分线的交点,连接这些点形成角平分线的一部分。
以上提示语为根据原始绘图命令整理而来,仅供参考。