垂直角的缺失值计算:几何作图与角度性质
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本范例演示如何通过几何作图计算垂直角的缺失值。核心数学概念包括垂直角的性质、角度测量与代数求解。作图要点涉及使用GeoGebra命令如Element、Angle和Textfield来构造垂直角图形,并利用If和Polygon命令进行动态调整。适合6-8年级学生用于几何练习和课堂演示。
GeoGebra 命令及参数
Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNumShuffle(Sequence[t, t, 20, angBig - 10, 2]) → allAngMini2, {20, 152, 22, 158, 86, 104, 38, 96, 140, 80, 44, 154, 162, 138, 130, 58, 26, 144, 46, 108, 52, 34, 122, 136, 102, 112, 150, 64, 72, 164, 148, 74, 132, 88, 54, 160, 76, 156, 62, 30, 126, 90, 84, 36, 94, 168, 128, 92, 98, 120, 78, 142, 134, 116, 100, 70, 42, 110, 60, 32, 40, 28, 146, 50, 82, 66, 166, 114, 106, 56, 48, 170, 124, 68, 24, 118}Shuffle(Sequence[t, t, 21, angBig - 12, 3]) → allAngMini3, {21, 39, 147, 165, 105, 102, 45, 126, 123, 93, 60, 150, 162, 129, 153, 48, 72, 30, 81, 96, 84, 90, 33, 51, 24, 57, 135, 99, 138, 111, 114, 144, 78, 36, 117, 108, 63, 156, 75, 69, 132, 87, 120, 141, 168, 42, 66, 27, 54, 159}Element(allAngMini2, Mod[countQuestion, Length[allAngMini2]] + 1) → angMini2Element(allAngMini3, Mod[countQuestion, Length[allAngMini3]] + 1) → angMini3Rotate(A, If[caseNum ≟ 1, angMini2°, angMini3°], O) → BAngle(A, O, B) → angAOBTextfield(input1) → InputBox1TextToUnicode(("" * InputBox1)) → studUniCurrentRotate(A, angBig°, O) → AFAngle(B, O, AF) → angBOFIf(caseNum ≟ 1, angMini2 / 2, angMini3 / 3) → ans1Angle(A, O, AF) → bigATextfield(input2) → InputBox2Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBoxCorner(5) → layoutAppSizeonboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffsetElement({If[layoutX ≟ 16, layoutX - 5, 11], layoutX - 5}, layoutCase) → layoutHintSolnXPoint(Vector[(1.8 * UnitVector[AngularBisector[AA, O, BB]])], 1) → posLabelAOBPoint(Vector[(4.4 * UnitVector[AngularBisector[AA, O, AFF]])], 1) → posLabBigSegment(O, AF) → vertSegment(O, A) → horSegment(O, B') → angSidePoint(Vector[(1.8 * UnitVector[AngularBisector[B', O, AF]])], 1) → posLabelSol2Angle(A, O, B') → solCase1Point(Vector[(1.8 * UnitVector[AngularBisector[A, O, B']])], 1) → posLabelSol1Point(Vector[(2.2 * UnitVector[AngularBisector[BB, O, AFF]])], 1) → posLabelBOFMirror(B, O) → BOSegment(O, BO) → angSide2Angle(AF, O, BO) → angVertIf(showhint, 3, 0) → speedRotate(A, If[caseNum ≟ 1, ((2 * aniSli) * input1°), ((3 * aniSli) * input1°)], O) → SASegment(O, SA) → studSideAngle(A, O, SA) → studAng
AI 绘图提示语参考
在同一坐标系中先放置点A、B两条射线并标出以O为顶点的角度。以O为中心构造一条水平参考线从O指向A,并给出另一条射线从O经过B;再在O处量出∠AOB并显示角度读数。提供一个输入框用于填写未知的角值input1,同时再画一条从A绕O旋转得到的射线AF,并在O处标出∠BOF与∠AOF等相关角度。最后以O为端点画出从O到AF的线段,并对称画出与B关于O的对应射线,用于形成竖直方向的角∠AF与该对称射线所夹的角,并把学生答案与提示区域以文字框形式呈现。
以上提示语为根据原始绘图命令整理而来,仅供参考。