平行四边形面积计算 by Ooi Soo Huat
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向量法计算平行四边形面积;②涉及核心概念:向量叉积、坐标几何、几何作图;③构造要点:使用Line, Point, Vector, Midpoint, Segment等命令绘制图形并计算面积;④适合高中数学教学和学生自主探究几何问题。
GeoGebra 命令及参数
Line(A, yAxis) → bLine(A, xAxis) → aPoint(a) → BDistance(A, B) → ABLine(B, b) → cPoint(c) → CLine(C, a) → dPoint(d) → GIntersect(b, d) → DIf(NearC ≟ true, C, G) → PmDynamicCoordinates(G, x(Pm), y(Pm)) → ELine(E, c) → gIntersect(a, g) → HCircle(E, AB) → eIntersect(e, d, 1) → FLine(F, b) → hIntersect(a, h) → IDistance(C, E) → ECDistance(E, H) → EHIf(E_B ≟ true, Polygon[E, B, H], Polygon[E, B, C]) → poly1Polygon(I, B, C, F) → poly2, i, b_2, c_2, fIf(E_B ≟ true, Polygon[F, A, D], Polygon[F, A, I]) → poly3Polygon(A, H, E, D) → poly4, a_1, h_1, e_1, d_1Polygon(A, B, C, D) → poly5, a_2, b_1, c_1, d_2Vector(C, D) → uIf(E_R ≟ true, Translate[poly1, Vector[(m * u)]], Translate[poly3, Vector[(m * (-u))]]) → TransMidpoint(D, A) → JLine(J, a) → jCircle(J, n) → kIntersect(k, j, 1) → KLine(K, h) → lCircle(K, n) → pIntersect(p, l, 2) → LIntersect(p, l, 1) → MIntersect(d, l) → NIntersect(a, l) → OVector(M, O) → vVector(L, N) → wMidpoint(A, B) → PCircle(P, n) → qLine(P, c) → rIntersect(q, r, 1) → QLine(Q, j) → sCircle(Q, n) → tIntersect(t, s, 1) → RIntersect(t, s, 2) → SIntersect(c, s) → TIntersect(b, s) → UVector(R, U) → u_1Vector(S, T) → v_1Intersect(j, c) → VCircle(V, n) → f_1Intersect(f_1, c) → W, ZSegment(D, C) → k_1Segment(C, B) → l_1Segment(B, A) → m_1Intersect(f_1, j, 2) → A_1Line(A_1, r) → g_1Circle(A_1, n) → p_1Intersect(p_1, g_1, 2) → B_1Intersect(p_1, g_1, 1) → C_1Intersect(d, g_1) → D_1Intersect(a, g_1) → E_1Vector(B_1, D_1) → w_1Vector(C_1, E_1) → i_1Segment(A, D) → j_1Angle(A, D, C) → αAngle(C, B, A) → β
AI 绘图提示语参考
绘制一个平行四边形及其面积计算辅助图形。先画两条互相垂直的坐标轴,在横轴上取一点作为平行四边形的一个顶点,过该点作纵轴的平行线,再在平行线上取一点作为另一顶点,过该点作横轴的平行线,与纵轴交于一点,形成平行四边形。然后构造多个辅助三角形和四边形,通过平移和旋转展示面积关系,并画出对角线向量、中点、圆和交点,最终用不同颜色区分各多边形区域,以直观演示面积公式。
以上提示语为根据原始绘图命令整理而来,仅供参考。