三角形中线演示
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①本范例演示了三角形中线的性质与构造;②涉及的核心数学概念包括三角形中线、重心、角平分线、垂线等;③作图要点提炼自构造摘要,使用了Polygon、midtri、Line、Angle、Intersect、Distance、OrthogonalLine、Segment、Midpoint、Circle、AngularBisector等GeoGebra命令/对象;④适合高中数学教学或几何爱好者学习使用。
GeoGebra 命令及参数
Polygon(A, B, C) → poly1, c, a, bPolygon(D, E, F) → poly2, f, d, emidtri(F, D, E) → G, H, I, poly3midtri(I, G, H) → J, K, L, poly4midtri(K, L, J) → M, N, O, poly5midtri(N, O, M) → P, Q, R, poly6Line(A, H) → iLine(B, I) → jLine(C, G) → kAngle(F, A, E) → αAngle(C, B, A) → βAngle(A, C, B) → γAngle(E, D, F) → δAngle(F, E, D) → εAngle(D, F, E) → ζAngle(C, D, E) → ηAngle(D, E, C) → θAngle(E, F, A) → ιAngle(A, E, F) → κAngle(B, F, D) → λAngle(F, D, B) → μLine(S, A) → mLine(S, C) → nLine(S, B) → pIntersect(p, b) → TDistance(A, T) → distanceATDistance(T, C) → distanceTCIntersect(m, a) → UIntersect(n, c) → VDistance(A, V) → distanceAVDistance(V, B) → distanceVBDistance(B, U) → distanceBUDistance(U, C) → distanceUCOrthogonalLine(S, b) → qOrthogonalLine(S, c) → rOrthogonalLine(S, a) → sIntersect(s, a) → WIntersect(q, b) → ZIntersect(r, c) → A_1Segment(A_1, S) → tSegment(W, S) → a_1Segment(Z, S) → b_1Angle(S, A_1, A) → νAngle(C, W, S) → ξAngle(A, Z, S) → οMidpoint(a) → B_1Midpoint(c) → C_1Midpoint(b) → D_1OrthogonalLine(C_1, c) → c_1OrthogonalLine(D_1, b) → d_1OrthogonalLine(B_1, a) → e_1Intersect(c_1, d_1) → E_1Segment(E_1, B) → f_1Segment(E_1, A) → g_1Segment(E_1, C) → h_1Circle(E_1, B) → k_1AngularBisector(C, B, A) → i_1AngularBisector(B, A, C) → j_1AngularBisector(A, C, B) → l_1Intersect(i_1, j_1) → F_1Angle(F_1, C, B) → ρAngle(A, C, F_1) → σ
AI 绘图提示语参考
画一个三角形,并展示其三条中位线。在中位线上找到中点,并连接这些中点形成一个新的三角形。标注原三角形的顶点和中位线的中点,并画出从顶点到中位线的线段。测量并显示这些线段的长度,以及新三角形与原三角形的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。