三角形的中线、重心、高线和垂心
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本范例演示了三角形的中线、重心、高线和垂心的概念。通过构造三角形的中线、高线和垂心,可以直观地理解这些几何元素的性质。使用了Polygon, Angle, Circle, Intersect, Line, Segment, Distance, Midpoint等GeoGebra命令。适合初中及以上学生学习三角形几何。
GeoGebra 命令及参数
Polygon(A, B, C) → poly1, c, a, bAngle(B, A, C) → αAngle(A, C, B) → βAngle(C, B, A) → γCircle(A, B) → dCircle(B, A) → eIntersect(d, e, 2) → DIntersect(d, e, 1) → ELine(D, E) → fCircle(A, C) → gCircle(C, A) → hIntersect(g, h, 2) → FIntersect(g, h, 1) → GLine(F, G) → iCircle(C, B) → kCircle(B, C) → pIntersect(k, p, 2) → HIntersect(k, p, 1) → ILine(H, I) → jIntersect(f, c) → JIntersect(i, b) → KIntersect(j, a) → LSegment(A, L) → lSegment(B, K) → mSegment(J, C) → nIntersect(l, m) → MCircle(A, B) → qCircle(C, B) → rIntersect(q, r, 2) → NLine(B, N) → sIntersect(s, b) → OCircle(B, A) → tCircle(C, A) → c_1Intersect(t, c_1, 2) → PLine(A, P) → f_1Intersect(f_1, a) → QSegment(B, O) → g_1Segment(A, Q) → h_1Circle(A, B) → d_1Circle(B, C) → e_1Intersect(d_1, e_1, 2) → RLine(R, C) → i_1Intersect(i_1, c) → SSegment(C, S) → j_1Angle(N, O, A) → δAngle(A, Q, B) → εCircle(A, C) → k_1Circle(B, C) → p_1Intersect(k_1, p_1, 2) → TLine(T, C) → l_1Intersect(l_1, c) → UAngle(A, U, T) → ζSegment(U, C) → m_1Intersect(s, f_1) → VDistance(A, M) → AMDistance(A, M) → distanceAMDistance(C, M) → distanceCMDistance(B, A) → distanceBADistance(L, A) → distanceLADistance(M, l) → distanceMlDistance(L, M) → distanceLMDistance(C, J) → distanceCJDistance(M, J) → distanceMJDistance(B, K) → distanceBKDistance(B, M) → distanceBMDistance(B, K) → oDistance(B, M) → uDistance(B, K) → vDistance(M, K) → distanceMKDistance(B, M) → wDistance(M, K) → a_1Distance(B, K) → b_1Distance(L, A) → n_1Distance(A, M) → o_1Distance(L, M) → q_1Distance(A, Q) → distanceAQDistance(A, V) → distanceAVDistance(V, Q) → distanceVQDistance(B, O) → distanceBODistance(B, V) → distanceBVDistance(V, O) → distanceVODistance(C, J) → r_1Midpoint(C, J) →Distance(C, M) → s_1Midpoint(C, M) →Distance(M, J) → t_1Midpoint(M, J) →Distance(C, U) → distanceCUMidpoint(C, U) →Distance(C, V) → distanceCVMidpoint(C, V) →Distance(V, U) → distanceVUMidpoint(V, U) →
AI 绘图提示语参考
绘制一个三角形ABC,然后画出它的三条中线、三条高和三条中垂线,标记出重心、垂心和外心。首先画出三角形,接着画出每个顶点到对边中点的中线,然后画出每个顶点到对边的垂线,最后画出每个顶点到对边中点的中垂线,标记出它们的交点。
以上提示语为根据原始绘图命令整理而来,仅供参考。