三角形的对称点
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①本范例演示了如何在三角形中找到对称点;②涉及的核心数学概念包括对称轴、中点、角平分线、线段、点、镜像、交点等;③作图要点——使用了Polygon(多边形)、Midpoint(中点)、AngularBisector(角平分线)、Segment(线段)、Point(点)、Mirror(镜像)、Intersect(交点)等GeoGebra命令和对象;④适合高中数学教学和几何作图学习。
GeoGebra 命令及参数
Polygon(M, N, O) → poly3, o, m_1, nMidpoint(m_1) → Midpoint''Midpoint(o) → MidpointMidpoint(n) → Midpoint'Polygon(P, Q, R) → poly4, r, p, qMidpoint(r) → SMidpoint(q) → TMidpoint(p) → UAngularBisector(P, R, Q) → c_1AngularBisector(Q, P, R) → d_1Segment(Q, T) → Median''Segment(U, P) → MedianSegment(S, R) → Median'AngularBisector(P, Q, R) → sPolygon(J, K, L) → poly2, l_1, j_1, k_1Point(k_1) → WSegment(W, K) → jPoint(l_1) → GSegment(G, L) → kAngularBisector(J, K, L) → a_1AngularBisector(J, L, K) → b_1AngularBisector(K, J, L) → e_1Mirror(W, a_1) → W'Mirror(K, a_1) → K'Segment(W', K') → SymmedianMirror(J, e_1) → J'Mirror(G, b_1) → G'Mirror(L, b_1) → L'Segment(G', L') → Symmedian'Midpoint(j_1) → B_1Segment(J, B_1) → tMirror(J, e_1) → J'_3Mirror(B_1, e_1) → ZSegment(J'_3, Z) → Symmedian''Polygon(J_1, K_1, L_1) → poly2_1, l_2, j_2, k_2Point(k_2) → W_1Segment(W_1, K_1) → j_3Point(l_2) → G_1Segment(G_1, L_1) → k_3AngularBisector(J_1, K_1, L_1) → a_3AngularBisector(J_1, L_1, K_1) → b_2AngularBisector(K_1, J_1, L_1) → e_2Mirror(W_1, a_3) → W'_1Mirror(K_1, a_3) → K'_1Segment(W'_1, K'_1) → Symmedian_1Mirror(G_1, b_2) → G'_1Mirror(L_1, b_2) → L'_1Segment(G'_1, L'_1) → Symmedian'_1Midpoint(j_2) → B_2Segment(J_1, B_2) → t_1Mirror(J_1, e_2) → J'_4Mirror(B_2, e_2) → Z_1Segment(J'_4, Z_1) → t'_1Intersect(l_2, Symmedian'_1) → HIntersect(k_2, Symmedian_1) → VIntersect(j_2, t'_1) → A_1Segment(K_1, V) → f_1Segment(J_1, A_1) → g_1Segment(H, L_1) → h_1Polygon(J_2, K_2, L_2) → poly2_2, l_3, j_4, k_4Point(k_4) → W_2Segment(W_2, K_2) → j_5Point(l_3) → G_2Segment(G_2, L_2) → k_5AngularBisector(J_2, K_2, L_2) → a_2AngularBisector(J_2, L_2, K_2) → b_3AngularBisector(K_2, J_2, L_2) → e_3Mirror(W_2, a_2) → W'_2Mirror(K_2, a_2) → K'_2Segment(W'_2, K'_2) → Symmedian_2Mirror(G_2, b_3) → G'_2Mirror(L_2, b_3) → L'_2Segment(G'_2, L'_2) → Symmedian'_2Midpoint(j_4) → B_3Segment(J_2, B_3) → t_2Mirror(J_2, e_3) → J'_1Mirror(B_3, e_3) → Z_2Segment(J'_1, Z_2) → t'_2Intersect(l_3, Symmedian'_2) → H_1Intersect(k_4, Symmedian_2) → V_1Intersect(j_4, t'_2) → A_2Segment(K_2, V_1) → f_2Segment(J_2, A_2) → g_2Segment(H_1, L_2) → h_2Intersect(f_2, g_2) → SYMMEDIANPOINTPolygon(J_3, K_3, L_3) → poly2_3, l_4, j_6, k_6Point(k_6) → W_3Segment(W_3, K_3) → j_7Point(l_4) → G_3Segment(G_3, L_3) → k_7AngularBisector(J_3, K_3, L_3) → a_4AngularBisector(J_3, L_3, K_3) → b_4AngularBisector(K_3, J_3, L_3) → e_4Mirror(W_3, a_4) → W'_3Mirror(K_3, a_4) → K'_3Segment(W'_3, K'_3) → Symmedian_3Mirror(G_3, b_4) → G'_3Mirror(L_3, b_4) → L'_3Segment(G'_3, L'_3) → Symmedian'_3Midpoint(j_6) → B_4Segment(J_3, B_4) → t_3Mirror(J_3, e_4) → J'_2Mirror(B_4, e_4) → Z_3Segment(J'_2, Z_3) → t'_3Intersect(l_4, Symmedian'_3) → H_2Intersect(k_6, Symmedian_3) → V_2Intersect(j_6, t'_3) → A_3Segment(K_3, V_2) → f_3Segment(J_3, A_3) → g_3Segment(H_2, L_3) → h_3Intersect(f_3, g_3) → SYMMEDIANPOINT'Midpoint(l_4) → BMidpoint(k_6) → CMidpoint(j_6) → DSegment(K_3, C) → aSegment(J_3, D) → bSegment(B, L_3) → cIntersect(a, b) → CENTROID
AI 绘图提示语参考
画一个三角形,标出三个顶点,分别求出每条边的中点和角平分线,连接顶点和对应边的中点得到三条中线,再求出每条角平分线与对边的交点,连接顶点和交点得到三条角平分线,最后求出三条中线的交点即三角形的对称点,并画出由对称点与角平分线交点构成的四边形和五边形。
以上提示语为根据原始绘图命令整理而来,仅供参考。