菱形(Deltoid)几何构造练习
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本范例演示如何用GeoGebra构造菱形(Deltoid)这一特殊四边形。核心数学概念包括菱形的定义、性质(四条边相等、对角线互相垂直平分)以及特殊四边形的分类。作图要点:使用Polygon命令绘制多边形,通过Angle命令测量角度验证菱形性质,利用Segment命令绘制边,用Stretch进行图形变换,结合If条件判断和Textfield文本框实现交互练习。适合5-6年级学生掌握基本几何作图工具(圆规、直尺、量角器或DGS)的使用,培养构造特殊四边形的能力。
GeoGebra 命令及参数
Join(Sequence[Join[{Shuffle[Sequence[1, 7]], Shuffle[Sequence[8, 14]]}], m, 1, 9]) → listExNumsIf(Mod[exnum, 7] ≟ 0, 7, Mod[exnum, 7]) → typElement({10, 10, 9, 9, 8, 8, 12}, typ) → maxstepElement({M1, M2, M3, M4, M5, M6, M7, M8, M9, M10, M11, M12, M13, M14}, exnum) → MTextfield(input1) → InputBox1Textfield(input2) → InputBox2Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 5, 7, 7, 4, 0, 2, 5, 9, 8, 0, 9, 4, 7, 5, 2, 7, 10, 5, 0, 2, 10, 1, 3, 2, 8, 10, 4, 1, 7, 6, 6, 3, 5, 1, 6, 10, 9, 3, 5, 2, 1, 5, 1, 7, 8, 7, 2, 2, 10, 5, 9, 7, 5, 5, 6, 10, 8, 0, 3, 2, 9, 5, 0, 2, 7, 2, 0, 1, 8, 5, 3, 6, 0, 5, 4, 4, 9, 6, 1, 10, 4, 5, 8, 5, 1, 5, 0, 8, 0, 1, 3, 2, 2, 7, 4, 6, 0, 1, 1}Element(randomNosForX, Mod[questionCount, 100] + 1) → numXShuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 9, 6, 6, 2, 3, 4, 1, 7, 5, 7, 10, 2, 7, 4, 1, 4, 2, 9, 8, 5, 9, 5, 6, 0, 10, 3, 6, 2, 5, 5, 8, 2, 5, 8, 1, 1, 2, 7, 6, 6, 10, 10, 9, 4, 5, 2, 2, 3, 6, 4, 7, 5, 7, 5, 6, 2, 6, 10, 6, 5, 5, 7, 4, 9, 8, 4, 7, 1, 2, 7, 0, 10, 1, 0, 4, 10, 5, 5, 10, 6, 10, 5, 8, 6, 5, 8, 5, 2, 1, 8, 3, 1, 1, 2, 3, 6, 9, 0, 9}Element(randomNosForY, Mod[questionCount, 100] + 1) → numYAppend(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayXAppend(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayYRemove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeatRemove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeatElement(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeatElement(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeatDefined((input1 * input2)) → fixedAngle(B, A, D) → walphaAngle(C, B, A) → wbetaLaTeX(typ, true, true) → Text3Segment(A, B) → a1Segment(A, D) → a2Segment(B, C) → b1Segment(C, D) → b2Segment(A, M) → eoSegment(M, C) → euSegment(B, D) → fZip(If[m < 5, " cm", "°"], m, numValues) → listEHAngle(A, D, C) → wdeltaAngle(D, C, B) → wgammaStretch(A, Line[B, D], 1.2) → A'Stretch(C, Line[B, D], 1.2) → C'Segment(A', C') → elangStretch(B, Line[A, C], 1.3) → B'Stretch(D, Line[A, C], 1.3) → D'Segment(B', D') → flangAngle(A, M, B) → rechterwinkelStretch(B, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → B'_{1}Stretch(C, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → C'_{1}Segment(B'_{1}, C'_{1}) → b1langStretch(C, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → C'_{2}Stretch(D, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → D'_{1}Segment(C'_{2}, D'_{1}) → b2langStretch(A, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → A'_{1}Stretch(D, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → D'_{2}Segment(A'_{1}, D'_{2}) → a2langStretch(A, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → A'_{2}Stretch(B, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → B'_{2}Segment(A'_{2}, B'_{2}) → a1langElement({2, 1, 3, 3, 4, 3, 4}, typ) → numCheckValueIf((checkValue * 10) - floor((checkValue * 10)) ≥ 0.5, (floor((checkValue * 10)) * 0.1) + 0.1, (floor((checkValue * 10)) * 0.1)) → checkValueGerundetIf(step ≟ 1, G_1, G_2) → GIf(step ≟ 1, H_1, H_2) → HAngle(B, M, C) → rechterwinkel2
AI 绘图提示语参考
画一个风筝形状的图形,四条边长度相等,对角线互相垂直且平分。先绘制一个四边形,确保四条边长度相同,然后用工具测量对角线的交角,验证它们是否为直角。接着,将四边形的一对对角线向外拉伸,使图形变形,同时保持四条边长度不变,观察对角线的变化。最后,在四边形内部绘制两条对角线,并标注它们的交点和关键角度,展示风筝的几何特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。