探索平行线与截线的变换
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本范例通过平移变换探索平行线与截线的性质。演示了平行线与截线的几何关系,涉及的核心数学概念包括平行线、截线及其交点。使用了Line, Point, Circle, Intersect, If等GeoGebra命令进行构造。适合初中及以上学生学习几何变换。
GeoGebra 命令及参数
Line(A, B) → fLine(C, f) → gPoint(f) → DLine(D, C) → hCircle(C, 0.5) → dCircle(D, 0.5) → cIntersect(c, f) → E, FIntersect(c, h) → G, HIntersect(d, h) → I, JIntersect(d, g) → K, LIntersect(i, f) → MIntersect(i, g) → NIf(y(N) > y(M), CircleSector[C, I, L], CircleSector[C, J, L]) → tIf(y(N) > y(M), CircleSector[C, K, I], CircleSector[C, K, J]) → sIf(y(N) > y(M), CircleSector[C, J, K], CircleSector[C, I, K]) → rIf(y(N) > y(M), CircleSector[D, F, H], CircleSector[D, F, G]) → qIf(y(N) > y(M), CircleSector[D, G, F], CircleSector[D, H, F]) → pIf(y(N) > y(M), Angle[E, D, G], Angle[E, D, H]) → αIf(y(N) > y(M), Angle[H, D, E], Angle[G, D, E]) → βIf(y(N) > y(M), Angle[F, D, H], Angle[F, D, G]) → γIf(y(N) > y(M), Angle[G, D, F], Angle[H, D, F]) → δIf(y(N) > y(M), Angle[J, C, K], Angle[I, C, K]) → εIf(y(N) > y(M), CircleSector[D, E, G], CircleSector[D, E, H]) → kIf(y(N) > y(M), CircleSector[D, H, E], CircleSector[D, G, E]) → eIf(y(N) > y(M), CircleSector[C, L, J], CircleSector[C, L, I]) → c_1If(y(N) > y(M), Angle[K, C, I], Angle[K, C, J]) → ζIf(y(N) > y(M), Angle[I, C, L], Angle[J, C, L]) → ηIf(y(N) > y(M), Angle[L, C, J], Angle[L, C, I]) → θ