梯形折叠演示
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①本范例演示梯形折叠后的几何变换与性质;②涉及核心数学概念包括多边形、几何变换(旋转)、中点、线段与圆弧;③构造要点:使用Polygon、Midpoint、CircleArc、Segment、Rotate、Intersect、OrthogonalLine、Line、Point等命令绘制并操作图形;④适合高中数学几何教学,用于理解梯形性质与变换关系。
GeoGebra 命令及参数
Polygon(A, C, D, B) → vierhoek1, a, c, d, bMidpoint(B, D) → BDMidpoint(A, C) → FMidpoint(B, E) → GCircleArc(B, DD, D) → eSegment(B, E) → fPolygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e_1Polygon(B, E, D) → driehoek1, d_1, b_2, e_2Rotate(B, (((-(s - 1)) * 180))°, e_1) → B'Rotate(E, (((-(s - 1)) * 180))°, e_1) → E'Rotate(D, (((-(s - 1)) * 180))°, e_1) → D'Polygon(B', E', D') → driehoek1', d', b', e'Polygon(DD, E, B) → driehoek2, b_3, dd, e_3Segment(G, F) → gPolygon(G, F, C, E) → vierhoek3, g_1, f_1, c_2, e_4Polygon(B, A, F, G) → vierhoek4, b_4, a_2, f_2, g_2Rotate(G, (((-(s - 3)) * 180))°, f_2) → G'Rotate(F, (((-(s - 3)) * 180))°, f_2) → F'Rotate(C, (((-(s - 3)) * 180))°, f_2) → C'Rotate(E, (((-(s - 3)) * 180))°, f_2) → E'_1Polygon(G', F', C', E'_1) → vierhoek3', g', f', c', e'_1Polygon(A, F, G, DD) → vierhoek5, a_3, f_3, g_3, dd_1Polygon(FE, A, F) → driehoek3, f_4, fe, a_4Segment(A, FA) → iRotate(FE, (((-(s - 5)) * 180))°, i) → FE'Rotate(A, (((-(s - 5)) * 180))°, i) → A'Rotate(F, (((-(s - 5)) * 180))°, i) → F'_1Polygon(B, A, FA, G) → vierhoek6, r, t, i_1, j_1Intersect(g_3, i) → HOrthogonalLine(H, g', xOyPlane) → jLine(BD, F) → nPoint(n) → KCircleArc(K, C, A) → pPolygon(G, H, F) → driehoek4, f_6, g_5, h_1Intersect(f_6, Line[FE, GG]) → JOrthogonalLine(H, b) → kCircleArc(A, F, FB) → hPolygon(A, F, FA) → driehoek5, fa, a_5, f_5Rotate(A, (((-(s - 5)) * 180))°, t) → A'_1Rotate(F, (((-(s - 5)) * 180))°, t) → F'_2Rotate(FA, (((-(s - 5)) * 180))°, t) → FA'Polygon(A'_1, F'_2, FA') → driehoek5', fa', a'_1, f'_2Line(DD, GG) → lIntersect(l, i) → IPolygon(G, DD, I, FA) → vierhoek7, g_4, dd_2, i_2, fa_1Line(FB, FA) → mIntersect(m, g_4) → MSegment(M, G) → qSegment(DD, I) → k_1Segment(DD, M) → l_1
AI 绘图提示语参考
画一个梯形,并展示其折叠后的几何变换。首先绘制梯形,然后找到其非平行边的中点,并连接这些中点形成新的四边形。接着,通过旋转操作模拟折叠过程,观察梯形在折叠后的形状变化和几何关系,包括旋转角度、中点连线、圆弧等元素。
以上提示语为根据原始绘图命令整理而来,仅供参考。