四边形的对称轴
几何画板及绘图内容加载中,请稍等……
①本范例演示如何寻找四边形的对称轴;②涉及的核心数学概念包括对称性、线段、角度、距离、反射变换;③作图要点——从下方『构造摘要』提炼用到了 Line, Segment, Angle, Distance, Point, Mirror, Intersect, Polygon, Circle, OrthogonalLine 等GeoGebra命令/对象;④适合初中及以上学生学习和探索几何对称性。
GeoGebra 命令及参数
Line(D, C) → fLine(B, C) → gSegment(B, C) → jSegment(C, D) → kLine(B, D) → mSegment(E, F) → pSegment(B, D) → tAngle(B, C, D) → γDistance(B, C) → distanceBCDistance(C, D) → distanceCDDistance(D, B) → distanceDBLine(J, K) → b_1Point(b_1) → LPoint(b_1) → NPoint(b_1) → OPoint(b_1) → QMirror(M, b_1) → M'Point(b_1) → PPoint(b_1) → RSegment(P, M) → c_1Segment(M, R) → f_1Segment(R, M') → g_1Segment(M', P) → h_1Segment(P, R) → i_1Segment(M, M') → j_1Intersect(i_1, j_1) → SLine(P, M') → k_1Line(M, R) → l_1Line(R, M') → m_1Line(M, P) → n_1Polygon(P, M, R, M') → poly3, p_1, m_2, r_1, m'Distance(P, M) → distancePMDistance(M, R) → distanceMRDistance(R, M') → distanceRM'Distance(M', P) → distanceM'PAngle(M', P, M) → ζAngle(P, M, R) → ηAngle(M, R, M') → θAngle(R, M', P) → ιAngle(P, S, M') → κDistance(M', M) → distanceM'MDistance(P, R) → distancePRSegment(T, U) → d_1Circle(S, Segment[U, T]) → e_1Point(e_1) → VLine(V, S) → q_1Mirror(P, q_1) → P'Mirror(M, q_1) → M'_1Mirror(R, q_1) → R'Mirror(M', q_1) → M''Polygon(P', M'_1, R', M'') → poly3', p', m'_1, r', m''Line(W, Z) → s_1Point(s_1) → B_1Point(s_1) → C_1Segment(B_1, C_1) → a_2Point(s_1) → D_1Point(s_1) → E_1Segment(D_1, E_1) → b_2Point(a_2) → H_1Line(A_1, F_1) → t_1Line(G_1, t_1) → c_2Point(c_2) → I_1Line(A_1, G_1) → h_2Line(F_1, I_1) → i_2Line(A_1, F_1) → j_2Line(I_1, G_1) → k_2Distance(G_1, A_1) → distanceG1A1Distance(A_1, F_1) → distanceA1F1Distance(F_1, I_1) → distanceF1I1Distance(I_1, G_1) → distanceI1G1Angle(I_1, G_1, A_1) → λAngle(G_1, A_1, F_1) → μAngle(A_1, F_1, I_1) → νAngle(F_1, I_1, G_1) → ξSegment(A_1, I_1) → l_2Segment(G_1, F_1) → n_2Intersect(l_2, n_2) → K_1Distance(G_1, F_1) → distanceG1F1Distance(A_1, I_1) → distanceA1I1Angle(G_1, K_1, I_1) → οPolygon(G_1, A_1, F_1, I_1) → poly4, g_2, a_3, f_2, i_3Segment(J_1, L_1) → d_2Circle(K_1, Segment[J_1, L_1]) → e_2Point(e_2) → M_1Line(K_1, M_1) → p_2Mirror(G_1, p_2) → N_1Mirror(A_1, p_2) → O_1Mirror(F_1, p_2) → P_1Mirror(I_1, p_2) → Q_1Polygon(N_1, O_1, P_1, Q_1) → poly4', n_3, o_1, p_3, q_2Line(R_1, S_1) → r_2Line(T_1, r_2) → s_2Segment(R_1, T_1) → t_2Circle(S_1, Segment[R_1, S_1]) → c_3Circle(S_1, Segment[R_1, T_1]) → d_3Circle(R_1, Segment[T_1, S_1]) → e_3Intersect(d_3, e_3, 2) → U_1Segment(T_1, U_1) → b_3Segment(U_1, S_1) → f_3Segment(S_1, R_1) → g_3Intersect(t_2, f_3) → V_1Intersect(b_3, g_3) → W_1Distance(U_1, V_1) → distanceU1V1Distance(U_1, W_1) → distanceU1W1Intersect(f_2, g_2) → Z_1Polygon(R_1, T_1, U_1, S_1) → poly5, r_3, t_3, u_1, s_3Line(R_1, T_1) → h_3Line(S_1, U_1) → j_3Line(T_1, U_1) → k_3Line(R_1, S_1) → l_3Segment(T_1, S_1) → m_3Segment(R_1, U_1) → q_3Intersect(m_3, q_3) → A_2Segment(B_2, C_2) → a_4Circle(A_2, Segment[B_2, C_2]) → c_4Point(c_4) → D_2Line(A_2, D_2) → b_4Mirror(R_1, b_4) → E_2Mirror(T_1, b_4) → F_2Mirror(U_1, b_4) → G_2Mirror(S_1, b_4) → H_2Polygon(E_2, F_2, G_2, H_2) → poly5', e_4, f_4, g_4, h_4Distance(R_1, T_1) → distanceR1T1Distance(T_1, U_1) → distanceT1U1Distance(U_1, S_1) → distanceU1S1Distance(S_1, R_1) → distanceS1R1Distance(R_1, U_1) → distanceR1U1Distance(T_1, S_1) → distanceT1S1Angle(R_1, A_2, S_1) → ρAngle(S_1, R_1, T_1) → σAngle(R_1, T_1, U_1) → τAngle(T_1, U_1, S_1) → υAngle(U_1, S_1, R_1) → ϕLine(I_2, J_2) → d_4Line(K_2, d_4) → i_4Line(K_2, I_2) → j_4Line(J_2, j_4) → k_4Intersect(i_4, k_4) → L_2Polygon(K_2, I_2, J_2, L_2) → poly6, k_5, i_5, j_5, l_4Line(I_2, K_2) → m_4Line(J_2, L_2) → n_4Line(I_2, J_2) → p_4Line(K_2, L_2) → q_4Segment(K_2, J_2) → r_4Segment(I_2, L_2) → s_4Intersect(r_4, s_4) → M_2Segment(N_2, O_2) → t_4Circle(M_2, Segment[N_2, O_2]) → c_5Point(c_5) → P_2Line(M_2, P_2) → a_5Mirror(K_2, a_5) → Q_2Mirror(I_2, a_5) → R_2Mirror(J_2, a_5) → S_2Mirror(L_2, a_5) → T_2Polygon(Q_2, R_2, S_2, T_2) → poly6', q_5, r_5, s_5, t_5Distance(I_2, K_2) → distanceI2K2Distance(K_2, L_2) → distanceK2L2Distance(L_2, J_2) → distanceL2J2Distance(J_2, I_2) → distanceJ2I2Distance(I_2, L_2) → distanceI2L2Distance(K_2, J_2) → distanceK2J2Angle(J_2, I_2, K_2) → χAngle(I_2, K_2, L_2) → ψAngle(K_2, L_2, J_2) → ωAngle(L_2, J_2, I_2) → α_1Angle(I_2, M_2, J_2) → β_1Distance(I_2, J_2) → distanceI2J2Distance(I_2, L_2) → v_1Distance(K_2, J_2) → w_1Circle(U_2, V_2) → d_5Point(d_5) → W_2Segment(V_2, W_2) → b_5Mirror(U_2, b_5) → Z_2Polygon(W_2, U_2, V_2, Z_2) → poly7, w_2, u_2, v_2, z_2Segment(U_2, Z_2) → e_5Intersect(b_5, e_5) → A_3Distance(W_2, V_2) → distanceW2V2Distance(U_2, Z_2) → distanceU2Z2Angle(W_2, A_3, Z_2) → γ_1Angle(Z_2, W_2, U_2) → δ_1Angle(W_2, U_2, V_2) → ε_1Angle(U_2, V_2, Z_2) → ζ_1Angle(V_2, Z_2, W_2) → η_1Distance(W_2, U_2) → distanceW2U2Distance(U_2, V_2) → distanceU2V2Distance(V_2, Z_2) → distanceV2Z2Distance(Z_2, W_2) → distanceZ2W2Segment(B_3, C_3) → f_5Circle(A_3, Segment[B_3, C_3]) → g_5Point(g_5) → D_3Line(D_3, A_3) → h_5Mirror(W_2, h_5) → E_3Mirror(U_2, h_5) → F_3Mirror(V_2, h_5) → G_3Mirror(Z_2, h_5) → H_3Polygon(E_3, F_3, G_3, H_3) → poly7', e_6, f_6, g_6, h_6Line(W_2, U_2) → l_5Line(U_2, V_2) → m_5Line(V_2, Z_2) → n_5Line(Z_2, W_2) → p_5Segment(I_3, J_3) → a_6OrthogonalLine(I_3, a_6) → b_6OrthogonalLine(J_3, a_6) → c_6Point(b_6) → K_3Line(K_3, b_6) → d_6Line(K_3, d_6) → i_6Line(K_3, a_6) → j_6Intersect(c_6, j_6) → L_3Polygon(I_3, K_3, L_3, J_3) → poly8, i_7, k_6, l_6, j_7Distance(I_3, K_3) → distanceI3K3Distance(K_3, L_3) → distanceK3L3Distance(L_3, J_3) → distanceL3J3Distance(J_3, I_3) → distanceJ3I3Angle(J_3, I_3, K_3) → θ_1Angle(I_3, K_3, L_3) → ι_1Angle(K_3, L_3, J_3) → κ_1Angle(L_3, J_3, I_3) → λ_1Segment(K_3, J_3) → m_6Segment(I_3, L_3) → n_6Intersect(m_6, n_6) → M_3Line(I_3, K_3) → p_6Line(K_3, L_3) → q_6Line(L_3, J_3) → r_6Line(J_3, I_3) → s_6Angle(I_3, M_3, J_3) → μ_1Distance(I_3, L_3) → distanceI3L3Distance(K_3, J_3) → distanceK3J3Segment(N_3, O_3) → t_6Circle(M_3, Segment[N_3, O_3]) → c_7Point(c_7) → P_3Line(M_3, P_3) → a_7Mirror(I_3, a_7) → Q_3Mirror(K_3, a_7) → R_3Mirror(L_3, a_7) → S_3Mirror(J_3, a_7) → T_3Polygon(Q_3, R_3, S_3, T_3) → poly8', q_7, r_7, s_7, t_7Segment(A, G) → aOrthogonalLine(A, a) → bOrthogonalLine(G, a) → cCircle(A, Segment[A, G]) → dCircle(G, Segment[A, G]) → eIntersect(d, b, 2) → HIntersect(e, c, 2) → IPolygon(A, H, I, G) → poly1, a_1, h, i, g_7Segment(H, G) → lSegment(I, A) → nIntersect(l, n) → U_3Line(H, I) → qLine(G, A) → rLine(A, H) → b_7Line(I, G) → d_7Angle(G, U_3, I) → αAngle(G, A, H) → βAngle(A, H, I) → δAngle(H, I, G) → εAngle(I, G, A) → ν_1Distance(A, H) → distanceAHDistance(H, I) → distanceHIDistance(I, G) → distanceIGDistance(G, A) → distanceGADistance(A, I) → distanceAIDistance(H, G) → distanceHGSegment(B, V_3) → e_7Segment(V_3, D) → f_7Polygon(V_3, B, C, D) → poly2, v_3, b_8, c_8, d_8Line(B, V_3) → h_7Line(V_3, D) → k_7Segment(C, V_3) → l_7Intersect(t, l_7) → W_3Intersect(c_8, v_3) → Z_3Intersect(d_8, b_8) → A_4Segment(B_4, C_4) → m_7Circle(W_3, Segment[B_4, C_4]) → p_7Point(p_7) → D_4Line(W_3, D_4) → n_7Mirror(V_3, n_7) → E_4Mirror(B, n_7) → B'Mirror(C, n_7) → C'Mirror(D, n_7) → D'Polygon(E_4, B', C', D') → poly2', e_8, b', c', d'Mirror(B', b') → B''Mirror(C', b') → C''Distance(V_3, B) → distanceV3BDistance(B, C) → z_1Distance(C, D) → o_2Distance(D, V_3) → distanceDV3Distance(V_3, C) → distanceV3CDistance(B, D) → distanceBDAngle(D, V_3, B) → ξ_1Angle(V_3, B, C) → ο_1Angle(B, C, D) → ρ_1Angle(C, D, V_3) → σ_1Angle(V_3, W_3, D) → τ_1Segment(F_4, G_4) → a_8Circle(U_3, Segment[F_4, G_4]) → f_8Point(f_8) → H_4Line(U_3, H_4) → g_8Mirror(A, g_8) → A'Mirror(H, g_8) → H'Mirror(I, g_8) → I'Mirror(G, g_8) → G'Polygon(A', H', I', G') → poly1', a', h', i', g'
AI 绘图提示语参考
画一个四边形,并找出它的对称轴。首先画出四边形的四条边和两条对角线,然后测量四边形的边长和角度。接着,找到对角线的中点,并画出其中一条对角线的垂线,这条垂线就是四边形的一条对称轴。最后,通过镜像变换,验证对称轴的对称性。
以上提示语为根据原始绘图命令整理而来,仅供参考。