测量 congruence
几何画板及绘图内容加载中,请稍等……
①本范例演示如何通过测量和变换验证图形的 congruence;②涉及核心数学概念包括 congruence、三维向量、梯形、向量、整数运算;③作图要点:使用 Segment、Rotate、Angle、Ray、Intersect、Polygon、Distance、Circle、Point、Line 等命令构建图形并进行变换;④适合高中学生或需要几何作图练习的学习者。
GeoGebra 命令及参数
Segment(A, B) → aRotate(B, 45*°, A) → B'Angle(B, A, B') → αRay(A, B') → bRotate(A, -100*°, B) → A'Angle(A', B, A) → βRay(B, A') → cIntersect(b, c) → CPolygon(A, B, C) → poly1, c_1, a_1, b_1Segment(D_1, E_1) → a_3Rotate(E_1, 45*°, D_1) → B'_1Angle(E_1, D_1, B'_1) → α_1Ray(D_1, B'_1) → b_3Rotate(D_1, -100*°, E_1) → A'_1Angle(A'_1, E_1, D_1) → β_1Ray(E_1, A'_1) → c_3Intersect(b_3, c_3) → F_1Polygon(D_1, E_1, F_1) → poly1_1, c_2, a_2, b_2Distance(A, C) → distanceACDistance(B, C) → distanceBCDistance(A, B) → distanceABRotate(D_1, 45*°, E_1) → DRotate(E_1, 45*°, E_1) → ERotate(F_1, 45*°, E_1) → FPolygon(D, E, F) → poly2, f', d', e'Circle(A, 10) → dPoint(d) → GCircle(D, 10) → ePoint(e) → HCircle(B, 10) → gPoint(g) → ICircle(E, 10) → hPoint(h) → JCircle(A, 5) → pPoint(p) → KLine(K, A) → mIntersect(p, m, 2) → LCircle(D, 5) → qPoint(q) → MLine(M, D) → nIntersect(q, n, 2) → NCircle(C, 5) → rCircle(F, 5) → sCircle(E, 5) → tCircle(B, 5) → d_1Point(d_1) → OPoint(r) → PPoint(t) → QPoint(s) → RLine(O, B) → e_1Line(P, C) → f_1Line(Q, E) → g_1Line(R, F) → h_1Intersect(d_1, e_1, 2) → SIntersect(r, f_1, 2) → TIntersect(t, g_1, 2) → UIntersect(s, h_1, 2) → VAngle(C, A, B) → γAngle(A, B, C) → δAngle(A, C, B) → εAngle(E, D, F) → ζAngle(F, E, D) → ηAngle(D, F, E) → θ
AI 绘图提示语参考
画一个几何图形,包含两个相似的梯形,通过旋转和测量验证它们的全等性。首先绘制一个梯形,然后将其一个顶点旋转45度并平移,得到另一个梯形。测量两个梯形对应边和角的大小,并标注关键点和线段。最后,在梯形的顶点绘制小圆,并添加辅助线和交点,展示全等性的验证过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。