三角形缩放演示
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①本范例演示了三角形经过缩放变换后的图形变化;②涉及核心数学概念包括缩放变换、相似三角形、距离计算;③作图要点使用了Polygon(多边形)、Dilate(缩放)、Ray(射线)、Distance(距离)等GeoGebra命令;④适合高中数学几何变换、相似性学习与探究。
GeoGebra 命令及参数
Polygon(B, C, D) → poly1, d, b, cDilate(B, a, A) → B'Dilate(C, a, A) → C'Dilate(D, a, A) → D'Polygon(B', C', D') → poly1', d', b', c'Ray(A, D) → eRay(A, B) → fRay(A, C) → gDistance(A, D) → distanceADDistance(A, D') → distanceAD'Distance(A, B) → distanceABDistance(A, B') → distanceAB'Distance(A, C) → distanceACDistance(A, C') → distanceAC'Distance(B, C) → distanceBCDistance(B', C') → distanceB'C'Distance(D', C') → distanceD'C'Distance(D, C) → distanceDCDistance(B, D) → distanceBDDistance(B', D') → distanceB'D'Dilate(B_1, a, A_1) → B'_1Dilate(D_1, a, A_1) → D'_1Ray(A_1, D_1) → e_1Ray(A_1, B_1) → f_1Distance(A_1, D_1) → distanceAD_1Distance(A_1, D'_1) → distanceAD'_1Distance(A_1, B_1) → distanceAB_1Distance(A_1, B'_1) → distanceAB'_1Distance(B_1, D_1) → distanceBD_1Distance(B'_1, D'_1) → distanceB'D'_1Dilate(B_2, a, A_2) → B'_2Dilate(C_1, a, A_2) → C'_1Ray(A_2, B_2) → f_2Ray(A_2, C_1) → g_1Distance(A_2, B_2) → distanceAB_2Distance(A_2, B'_2) → distanceAB'_2Distance(A_2, C_1) → distanceAC_1Distance(A_2, C'_1) → distanceAC'_1Distance(B_2, C_1) → distanceBC_1Distance(B'_2, C'_1) → distanceB'C'_1
AI 绘图提示语参考
绘制一个三角形ABC,然后以点A为中心,放大比例a,分别放大B、C、D得到三角形A'B'C'。接着画出从A出发的射线AD、AB、AC,以及AD、AD'、AB、AB'、AC、AC'、BC、B'C'、DC、BD、B'D'的长度。最后,以A'为中心,放大比例a,放大B1、D1得到B'_1、D'_1,画出从A'出发的射线D1A'、B1A',以及相关长度。
以上提示语为根据原始绘图命令整理而来,仅供参考。