横截线与平行线相交的探究活动
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①本范例演示横截线与平行线相交时形成的特殊角对关系;②涉及核心数学概念包括角、平行线、同位角、内错角、同旁内角等;③作图要点运用了Point, Circle, Intersect, Rotate, Angle, Line, Ray, Segment, CircleSector等GeoGebra命令和对象;④适合初中及以上数学教学,用于帮助学生直观理解平行线与横截线相交的几何性质。
GeoGebra 命令及参数
Point(f) → ACircle(A, 2) → cIntersect(c, f, 2) → BRotate(B, (a * π / 180), A) → B'Rotate(f, (b * π / 180), A) → f'Intersect(c, f', 2) → FRotate(F, (a * π / 180), A) → F'Angle(F, A, F') → αLine(A, F') → gIntersect(c, g, 1) → CRay(A, F') → hRay(A, C) → iIntersect(c, f', 1) → D_1Ray(A, F) → jRay(A, C) → kRay(A, D_1) → lPoint(l) → EPoint(h) → GPoint(k) → HPoint(j) → DLine(G, j) → mCircle(G, 1) → dIntersect(d, m) → J, KIntersect(d, h) → L, MRay(G, K) → nRay(G, J) → pPoint(n) → RPoint(p) → PIntersect(d, h, 2) → QRay(G, Q) → qSegment(A, G) → rPoint(q) → NCircle(G, 1.5) → c_1Circle(A, 1.5) → d_1Intersect(c_1, n, 1) → R_1Intersect(c_1, q, 1) → SIntersect(c_1, p, 1) → TIntersect(c_1, r, 1) → UIntersect(d_1, j, 1) → VIntersect(d_1, r, 1) → WIntersect(d_1, l) → Z,Intersect(d_1, k, 1) → A_1CircleSector(G, R_1, S) → e_1CircleSector(G, S, T) → f_1CircleSector(G, T, U) → g_1CircleSector(G, U, R_1) → h_1CircleSector(A, V, W) → k_1CircleSector(A, W, Z) → p_1CircleSector(A, Z, A_1) → q_1CircleSector(A, A_1, V) → r_1
AI 绘图提示语参考
画两条平行线,一条横线穿过它们,形成八个角。用圆和旋转工具找出对应角、内错角和同旁内角,并用射线和线段标示它们。再画圆和扇形来强调这些角的关系,最终展示平行线被横线截出的各种角形图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。