无字证明 by Steve Phelps (7)
几何画板及绘图内容加载中,请稍等……
所属专题
Similarity & Right Triangle Trigonometry
Similarity, Right Triangles, and Trigonometry (SRT) Cluster
Proofs Without Words
Proofs Without Words
Y10 Pythag & Trig
①本范例通过拖动点演示三角形与平行四边形的几何关系;②涉及核心概念:交点、平面图形、数列、方差、最小公倍数与最大公约数;③作图要点:使用Point, Intersect, Mirror, Segment, OrthogonalLine, Polygon, CircleArc, PointIn, Vector, Centroid, Translate, Midpoint等命令构建图形;④适合高中及以上学生及数学爱好者用于探索几何证明与变换。
GeoGebra 命令及参数
Point(xAxis) → AIntersect(xAxis, yAxis) → BMirror(A, B) → A'Segment(A, A') → h_1OrthogonalLine(A', h_1) → j_1Polygon(A', A, 4) → poly2, f, g, h, i, G, HCircleArc(B, C, A) → cPoint(c) → DPolygon(D, A', 4) → poly1, a, b, d, e, E, FOrthogonalLine(E, j_1) → p_1Intersect(j_1, p_1) → D_1OrthogonalLine(F, h_1) → i_1Intersect(i_1, p_1) → A_1OrthogonalLine(D, i_1) → q_1Intersect(j_1, q_1) → E_1Intersect(i_1, q_1) → F_1Polygon(F_1, A_1, D_1, E_1) → poly9, f_3, a_2, d_3, e_3PointIn(poly9) → KVector(K, G) → vOrthogonalLine(K, f) → nIntersect(n, poly1) → N, OOrthogonalLine(K, n) → pIntersect(p, poly1) → L, MPolygon(K, N, F, E, M) → poly4, k_1, n_1, f_1, e_1, m_1Centroid(poly4) → PTranslate(P, v) → P'Vector(P, P') → s_1Translate(E, s_1) → E'_2Polygon(A, D, 4) → poly3, j, k, l, m, I, JMidpoint(I, A) → ZPolygon(O, K, M, E, A') → poly7, o_1, k_4, m_2, e_2, a'_1Centroid(poly7) → SVector(K, A) → uTranslate(S, u) → S'Segment(S, S') → sPoint(s) → UVector(S, U) → v_1Translate(A', v_1) → A''Vector(A, E'_2) → r_1Translate(Z, r_1) → Z'Vector(K, H) → qVector(K, A') → wPolygon(L, D, A', O, K) → poly6, l_2, d_2, a', o, k_3Centroid(poly6) → RTranslate(R, w) → R'Polygon(L, D, F, N, K) → poly5, l_1, d_1, f_2, n_2, k_2Centroid(poly5) → QTranslate(Q, q) → Q'Polygon(S', R', Q', P') → poly8, s', r', q', p'Centroid(poly8) → C_1Segment(Q, Q') → rSegment(R, R') → tSegment(P, P') → a_1Point(a_1) → TVector(P, T) → u_1Point(t) → VVector(R, V) → w_1Point(r) → WVector(Q, W) → b_1Translate(L, b_1) → L'Translate(D, b_1) → D'Translate(F, b_1) → F'Translate(N, b_1) → N'Translate(K, b_1) → K'Polygon(L', D', F', N', K') → poly5', l', d', f', n', k'Translate(K, u_1) → K'_1Translate(N, u_1) → N'_1Translate(F, u_1) → F'_1Translate(E, u_1) → E'Translate(M, u_1) → M'Polygon(K'_1, N'_1, F'_1, E', M') → poly4', k'_1, n'_1, f'_1, e', m'Translate(O, v_1) → O'Translate(K, v_1) → K'_2Translate(M, v_1) → M'_1Translate(E, v_1) → E'_1Polygon(O', K'_2, M'_1, E'_1, A'') → poly7', o', k'_2, m'_1, e'_1, a''Translate(L, w_1) → L'_1Translate(D, w_1) → D'_1Translate(A', w_1) → A''_1Translate(O, w_1) → O'_1Translate(K, w_1) → K'_3Polygon(L'_1, D'_1, A''_1, O'_1, K'_3) → poly6', l'_1, d'_1, a''_1, o'_1, k'_3Segment(Z, Z') → c_1Point(c_1) → B_1Vector(Z, B_1) → g_1Translate(poly3, g_1) → poly3'
AI 绘图提示语参考
画一个几何图形,展示三角形与平行四边形的几何关系。通过拖动点观察变化,核心包含交点、平面图形、数字、变异数、最小公倍数和最大公约数。先画坐标轴交点,镜像生成对称点,连接形成平行四边形和四边形,再利用圆弧交点构造新图形,通过正交线、中点和重心进行平移变换,最终形成多个嵌套的多边形和连接线,体现几何变换与证明。
以上提示语为根据原始绘图命令整理而来,仅供参考。