平行四边形的对称轴 by سید مهدی بشارت
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①本范例演示平行四边形的对称轴及其性质;②涉及核心数学概念包括对称性、平行四边形性质、中点、旋转与镜像变换;③作图要点运用了PointIn, Polygon, Midpoint, Line, Circle, Intersect, Rotate, Mirror等GeoGebra命令与对象;④适合初中及以上学生学习几何变换与对称性,也可用于高中数学教学。
GeoGebra 命令及参数
PointIn(j) → BPointIn(j) → DPointIn(j) → CPointIn(j) → APolygon(A, B, C, D) → poly1, a, b, c, dMidpoint(a) → EMidpoint(c) → FMidpoint(d) → GMidpoint(b) → HLine(E, F) → fLine(G, H) → gLine(A, C) → hLine(D, B) → i_2Circle(H, 1, xOyPlane) → eCircle(B, 1, xOyPlane) → kCircle(E, 1, xOyPlane) → pCircle(C, 1, xOyPlane) → qIntersect(f, p, 1) → IIntersect(i_2, k, 2) → JIntersect(g, e, 2) → KIntersect(h, q, 2) → LCircle(I, 0.5, f) → rCircle(J, 0.5, i_2) → sCircle(K, 0.5, g) → tCircle(L, 0.5, h) → c_1Polygon(E, A, D, F) → poly2, e_1, a_1, d_1, f_1Polygon(E, B, C, F) → poly3, e_2, b_1, c_2, f_2Rotate(B, α, f) → B'Rotate(C, α, f) → C'Polygon(F, C', B', E) → poly4, f_3, c', b', e_3Polygon(G, D, C, H) → poly6, g_1, d_2, c_3, h_1Polygon(H, B, A, G) → poly7, h_2, b_2, a_2, g_2Rotate(C, (-α), g) → C'_1Rotate(D, (-α), g) → D'Polygon(D', G, H, C'_1) → poly8, d', g_3, h_3, c'_1Polygon(D, A, B) → poly9, b_3, d_3, a_3Polygon(D, B, C) → poly10, c_4, d_4, b_4Rotate(C, (-α), i_2) → C'_2Intersect(b, a) → QPolygon(C'_2, B, D) → poly11, d_5, c'_2, b_5Polygon(A, B, C) → poly12, c_5, a_4, b_6Polygon(A, C, D) → poly13, d_6, a_5, c_6Rotate(D, (-α), h) → D'_1Polygon(D'_1, A, C) → poly14, c_7, d'_1, a_6Intersect(g, f) → RIntersect(i_2, h) → SMirror(S, B) → S'Mirror(S, C) → S'_1Mirror(R, H) → R'Mirror(R, E) → R'_1Circle(R'_1, 0.25, xOyPlane) → k_1Circle(S', 0.25, xOyPlane) → p_1Circle(R', 0.25, xOyPlane) → q_1Circle(S'_1, 0.25, xOyPlane) → r_1Mirror(L, G) → L'Polygon(L', T, 4, xOyPlane) → poly15, i_1, j_1, l_1, m_1, U, V
AI 绘图提示语参考
画一个平行四边形,标出它的对角线和中点,然后画出通过中点的对称轴。以其中一条对角线为轴,将平行四边形旋转180度,观察旋转后的图形与原图重合。再以另一条对角线为轴,将平行四边形旋转180度,同样观察旋转后的图形与原图重合。最后,画出两条对角线交点处的圆,并标注关键点和线段,展示平行四边形的对称性和旋转变换特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。