角平分线与垂线的构造
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①本范例演示了如何通过 GeoGebra 构造三角形的角平分线与垂线;②涉及的核心数学概念包括角平分线、垂线、中线、旋转、镜像等;③作图要点——从下方『构造摘要』提炼用到了 LineBisector(角平分线)、Segment(线段)、Rotate(旋转)、Line(直线)、OrthogonalLine(垂线)、Intersect(交点)、Mirror(镜像)、CircleArc(圆弧)、Circle(圆)、Point(点)、Polygon(多边形)、Angle(角)、PointIn(点在...内)、Midpoint(中点)等 GeoGebra 命令/对象;④适合高中数学几何作图教学与学习。
GeoGebra 命令及参数
LineBisector(A, B) → l_4Segment(A, B) → fRotate(B, gam, A) → B'Line(A, B') → m_4OrthogonalLine(A, m_4) → n_4Intersect(l_4, n_4) → QMirror(Q, f) → Q'CircleArc(Q', B, A) → c_4Circle((A + B) / 2, B) → cPoint(c_4) → CLine(C, yAxis) → gLine(G, F) → hIntersect(g, h) → E_1Line(A, B) → iIntersect(i, g) → G_1Polygon(G, E_1, G_1, A) → ct1, d, e, g_1, a_1Polygon(E_1, F, B, G_1) → ct2, e_1, f_1, b_1, g_2Segment(A, G) → jSegment(B, F) → kLine(A, C) → lLine(C, B) → mOrthogonalLine(C, l) → nOrthogonalLine(A, l) → pOrthogonalLine(C, m) → qOrthogonalLine(B, m) → rPolygon(A, C, 4) → mnohoúhelník1, h_1, i_1, j_1, k_1, D, ELine(E, D) → l_1OrthogonalLine(B, l) → sOrthogonalLine(A, m) → tIntersect(s, l) → HIntersect(m, t) → IIntersect(l_1, s) → LPolygon(A, H, L, E) → ct3, a_2, h_2, l_2, k_2Polygon(H, C, D, L) → ct4, h_3, c_1, j_2, l_3Polygon(C, B, 4) → mnohoúhelník2, m_1, n_1, p_1, q_1, M, NLine(N, M) → r_1Intersect(t, r_1) → OPolygon(I, B, M, O) → ct5, i_2, b_2, m_2, oPolygon(C, I, O, N) → ct6, c_2, i_3, o_1, n_2Segment(A, H) → s_1Segment(H, C) → t_1Segment(C, D) → d_1Segment(D, L) → f_2Segment(L, E) → p_2Segment(E, A) → q_2Segment(L, H) → r_2Segment(G_1, E_1) → s_2Segment(G, E_1) → t_2Segment(E_1, F) → d_2Segment(C, I) → e_2Segment(I, B) → f_3Segment(B, M) → g_3Segment(M, O) → j_3Segment(O, I) → k_3Segment(N, O) → m_3Segment(N, C) → n_3Segment(G_1, A) → p_3Segment(C, G_1) → q_3Segment(H, B) → r_3Segment(A, I) → s_3Angle(A, C, B) → αPolygon(A, B, C) → t1, c_3, a_3, b_3PointIn(ct1) → Bodct1PointIn(ct6) → Bodct6_1PointIn(ct6) → Bodct6Segment(G, F) → t_3Segment(E, D) → d_3Segment(N, M) → e_3Segment(E, B) → f_4Segment(C, G) → g_4Segment(D, B) → h_4Segment(Bodct6, A) → i_4Segment(A, M) → j_4Segment(C, F) → k_4Midpoint(Bodct6, B) → KMidpoint(L, A) → PAngle(B, A, B') → βPolygon(B, A, 4) → mnohoúhelník3, p_4, q_4, r_4, s_4, R, SPolygon(C, B, 4) → mnohoúhelník4, t_4, a_4, b_4, d_4, T, UPolygon(A, C, 4) → mnohoúhelník5, e_4, f_5, g_5, h_5, V, WPolygon(C, B, 4) → mnohoúhelník6, i_5, j_5, k_5, l_5, Z, A_1Polygon(A, C, 4) → mnohoúhelník7, m_5, n_5, p_5, q_5, B_1, C_1
AI 绘图提示语参考
绘制一个三角形ABC,然后构造角平分线和垂直平分线。首先,构造角平分线AD和BE,接着构造垂直平分线DE。然后,找到三角形的外心Q,构造过Q的圆弧和圆。接着,构造三角形的中线和高,以及与之相关的垂线和交点。最后,根据这些线段和点,构造多个三角形和四边形,包括中点四边形、垂足四边形和外接圆等。
以上提示语为根据原始绘图命令整理而来,仅供参考。