对称轴 by Adam Bevan
几何画板及绘图内容加载中,请稍等……
这个范例演示了图形的对称轴。核心数学概念包括几何中的对称性。使用了GeoGebra命令如Segment, Line, Mirror, Intersect等来构造图形。适合初中及以上学生学习几何对称性。
GeoGebra 命令及参数
Segment(E, F) → pLine(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_2Intersect(f_2, g_2) → Z_1Segment(B_2, C_2) → a_4Line(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_4, C_4) → m_7Segment(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'Segment(B, C) → f
AI 绘图提示语参考
绘制一个几何图形,包含四边形PMRM'及其对称轴。首先画出线段PM,然后画出对称轴b1,接着画出点L、N、O、Q、P、R,利用镜像命令分别得到M'、P'、M'_1、R'、M'',最后画出四边形P'M'_1R'M''。
以上提示语为根据原始绘图命令整理而来,仅供参考。