四边形及其对角线
几何画板及绘图内容加载中,请稍等……
所属专题
Y7 Polygons
①本范例演示四边形的几何性质及其对角线的相关特性;②涉及的核心数学概念包括多边形、对角线、角、距离、几何作图等;③作图要点——从下方『构造摘要』提炼用到了 Line, Segment, Intersect, Distance, Circle, Point, OrthogonalLine, Mirror, Angle, Midpoint 等GeoGebra命令/对象;④适合高中阶段学习几何作图的学生或教师使用。
GeoGebra 命令及参数
Line(A, B) → aLine(C, a) → bSegment(C, A) → cLine(B, c) → dSegment(A, B) → eIntersect(b, d) → DSegment(C, D) → fSegment(D, B) → gDistance(A, B) → distanceABSegment(C, B) → iSegment(A, D) → jIntersect(i, j) → ECircle(G, F) → kSegment(G, F) → lPoint(k) → HSegment(G, H) → mLine(H, l) → nLine(F, m) → pIntersect(n, p) → ISegment(H, I) → qSegment(F, I) → rSegment(G, I) → sSegment(H, F) → tIntersect(s, t) → JSegment(K, L) → a_1OrthogonalLine(L, a_1) → b_1Point(b_1) → MOrthogonalLine(M, b_1) → c_1OrthogonalLine(K, a_1) → d_1Intersect(c_1, d_1) → NSegment(L, M) → e_1Segment(K, N) → g_1Segment(N, M) → f_1Segment(K, M) → h_1Segment(L, N) → i_1Intersect(h_1, i_1) → OCircle(P, Q) → k_1Segment(P, Q) → j_1OrthogonalLine(P, j_1) → l_1OrthogonalLine(Q, j_1) → m_1Intersect(k_1, l_1, 2) → SLine(S, j_1) → n_1Intersect(m_1, n_1) → RSegment(P, S) → p_1Segment(S, R) → q_1Segment(P, R) → s_1Segment(Q, S) → t_1Intersect(s_1, t_1) → TSegment(Q, R) → r_1Segment(W, U) → a_2Segment(U, V) → b_2Segment(V, W) → c_2Mirror(V, a_2) → XSegment(W, X) → d_2Segment(X, U) → e_2Segment(V, X) → f_2Intersect(a_2, f_2) → ZSegment(A_1, B_1) → g_2Segment(A_1, C_1) → h_2Line(C_1, g_2) → i_2Point(i_2) → D_1Segment(B_1, D_1) → j_2Segment(C_1, D_1) → k_2Segment(C_1, B_1) → l_2Segment(A_1, D_1) → m_2Intersect(l_2, m_2) → E_1Segment(C, E) → n_2Segment(E, B) → p_2Segment(D, E) → q_2Segment(E, A) → r_2Angle(A, B, E) → αAngle(E, B, D) → βAngle(B, D, E) → γAngle(E, D, C) → δAngle(D, C, E) → β_1Angle(E, C, A) → γ_1Angle(C, A, E) → δ_1Angle(E, A, B) → ε_1Angle(D, E, B) → ζ_1Segment(G, J) → s_2Segment(J, I) → t_2Segment(F, J) → a_3Segment(J, H) → b_3Angle(J, H, I) → εAngle(H, I, J) → ζAngle(J, I, F) → ηAngle(I, F, J) → θAngle(J, F, G) → η_1Angle(F, G, J) → θ_1Angle(J, G, H) → ι_1Angle(G, H, J) → κ_1Angle(I, J, H) → λ_1Segment(K, O) → c_3Segment(O, M) → d_3Segment(L, O) → e_3Segment(O, N) → f_3Angle(L, M, O) → ιAngle(O, M, N) → κAngle(M, N, O) → λAngle(O, N, K) → μAngle(N, K, O) → μ_1Angle(O, K, L) → ν_1Angle(K, L, O) → ξ_1Angle(O, L, M) → ο_1Angle(K, O, N) → ρ_1Segment(S, T) → g_3Segment(T, Q) → h_3Segment(P, T) → i_3Segment(T, R) → j_3Angle(T, S, R) → νAngle(S, R, T) → ξAngle(T, R, Q) → οAngle(R, Q, T) → ρAngle(T, Q, P) → σ_1Angle(Q, P, T) → τ_1Angle(T, P, S) → υ_1Angle(P, S, T) → φ_1Angle(Q, T, R) → χ_1Angle(X, Z, W) → σAngle(U, W, X) → τAngle(W, X, V) → υAngle(V, X, U) → φAngle(X, U, W) → ψ_1Angle(W, U, V) → ω_1Angle(U, V, X) → α_2Angle(X, V, W) → β_2Angle(V, W, U) → γ_2Segment(W, U) → k_3Segment(V, X) → l_3Midpoint(V, Z) → F_1Midpoint(Z, X) → G_1Distance(V, Z) → distanceVZDistance(V, Z) → oDistance(W, Z) → uDistance(U, Z) → vMidpoint(Z, W) → H_1Midpoint(U, Z) → I_1Segment(C_1, E_1) → m_3Segment(E_1, B_1) → n_3Segment(E_1, D_1) → p_3Segment(E_1, A_1) → q_3Angle(E_1, A_1, B_1) → χAngle(A_1, B_1, E_1) → ψAngle(E_1, B_1, D_1) → ωAngle(B_1, D_1, E_1) → α_1Angle(E_1, D_1, C_1) → δ_2Angle(D_1, C_1, E_1) → ε_2Angle(E_1, C_1, A_1) → ζ_2Angle(C_1, A_1, E_1) → η_2
AI 绘图提示语参考
绘制一个四边形ABCD,连接对角线AC和BD,标记它们的交点为E。然后以E为圆心,分别以A、B、C、D为圆周上的点画圆,标记圆的交点为F。接着画出四边形AEFD,连接对角线AF和DE,标记它们的交点为G。最后画出四边形AEGF,连接对角线AG和EF,标记它们的交点为H。
以上提示语为根据原始绘图命令整理而来,仅供参考。