平行四边形面积计算 by Lee W Fisher
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①本范例演示如何通过构造平行四边形并分割成三角形来计算其面积;②涉及核心数学概念包括平行四边形性质、三角形面积公式、几何变换;③作图要点使用了Polygon(多边形)、Point(点)、Segment(线段)、Midpoint(中点)、Circle(圆)、Rotate(旋转)、Angle(角度)、Ray(射线)、Intersect(交点)、OrthogonalLine(垂线)、Line(直线)等GeoGebra命令;④适合初中及以上学生学习平行四边形面积公式及几何作图方法。
GeoGebra 命令及参数
Polygon(A, B, C, D) → q1, a, b, c, dPoint(Circle[I, sqrt(45)]) → JSegment(I, J) → iMidpoint(I, J) → KCircle(K, J) → kRotate(J, atan(2), I) → J'Angle(J, I, J') → αRay(I, J') → jIntersect(k, j, 2) → LPolygon(I, L, J) → t1, j_1, i_1, lPoint(Circle[M, 6]) → NSegment(M, N) → nCircle(M, 7) → pOrthogonalLine(M, n) → qOrthogonalLine(N, n) → rIntersect(p, q, 2) → OOrthogonalLine(O, q) → sIntersect(r, s) → PRotate(P, atan(0.5), O) → P'Angle(P, O, P') → βRay(O, P') → tIntersect(r, t) → QPolygon(M, N, Q, O) → q3, m_1, n_1, q_1, oAngle(Q, N, M) → γPoint(Circle[E, 6]) → FSegment(E, F) → fOrthogonalLine(E, f) → gOrthogonalLine(F, f) → hPoint(h) → GPoint(Circle[G, 10]) → HSegment(G, H) → f_1Point(g) → RPoint(Circle[R, 10]) → SSegment(R, S) → g_1Polygon(G, R, S, H) → q2, g_2, r_1, s_1, h_1Angle(r_1, f) → δPoint(Circle[H_1, sqrt(116)]) → I_1Segment(H_1, I_1) → l_1Midpoint(H_1, I_1) → J_1Circle(J_1, I_1) → p_1Rotate(H_1, atan(2.5), I_1) → TAngle(H_1, I_1, T) → εRay(I_1, T) → t_1Intersect(p_1, t_1, 2) → UPolygon(H_1, I_1, U) → t2, u_1, h_2, i_2Point(Circle[V, 4]) → P_1Segment(V, P_1) → m_2Circle(P_1, sqrt(29)) → d_2Circle(V, sqrt(29)) → e_2Intersect(d_2, e_2, 1) → Q_1Line(Q_1, m_2) → n_2Segment(V, Q_1) → p_2Line(P_1, p_2) → q_2Intersect(n_2, q_2) → R_1Polygon(V, P_1, R_1, Q_1) → q5, v, p_3, r_2, q_3Point(Circle[S_1, 5]) → T_1Segment(S_1, T_1) → s_2OrthogonalLine(S_1, s_2) → t_2OrthogonalLine(T_1, s_2) → a_2Circle(S_1, 4) → c_3Intersect(c_3, t_2, 1) → U_1Circle(T_1, 2) → d_3Intersect(d_3, a_2, 1) → V_1Polygon(U_1, V_1, T_1, S_1) → q6, u_2, v_1, t_3, s_3Point(Circle[W, sqrt(29)]) → ZSegment(W, Z) → k_1Midpoint(W, Z) → A_1Circle(A_1, Z) → c_1Rotate(W, atan(2.5), Z) → W'Angle(W, Z, W') → ζRay(Z, W') → b_1Intersect(c_1, b_1, 2) → B_1Polygon(Z, B_1, W) → t3, w_1, z_1, b_2
AI 绘图提示语参考
绘制一个平行四边形,并将其分为两个三角形。首先,创建四个点A、B、C、D,然后使用这四个点创建一个平行四边形。接着,通过点C画一个圆,找到圆上的点J,连接I和J。然后,找到I和J的中点K,以K为圆心画一个圆。将J绕I旋转atan(2)弧度得到J',找到IJ'的夹角α。接着,画射线IJ',找到与圆K的第二个交点L,使用I、L、J创建一个三角形。继续画圆、旋转、找到新的交点和角度,直到完成整个图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。