三角形面积计算 by Ooi Soo Huat
几何画板及绘图内容加载中,请稍等……
所属专题
Mathematics Form 1
①本范例演示了如何通过 GeoGebra 动态计算三角形的面积;②涉及的核心数学概念包括解析几何、向量、多边形构造及几何作图;③作图要点提炼自构造摘要,使用了 Line, Point, Intersect, Polygon, Vector, Angle 等命令和对象;④适合高中数学教学,用于理解三角形面积公式及动态几何特性。
GeoGebra 命令及参数
Line(A, xAxis) → aLine(A, yAxis) → bPoint(a) → BLine(B, b) → cPoint(c) → CLine(C, a) → dPoint(d) → GIntersect(b, d) → DIf(NearC ≟ true, C, If[NearD ≟ true, D, G]) → PmDynamicCoordinates(G, x(Pm), y(Pm)) → EPolygon(A, E, B) → poly1, b_1, a_1, eOrthogonalLine(E, d) → fIntersect(a, f) → FPolygon(E, D, A) → poly2, a_2, e_1, d_1Polygon(E, C, B) → poly3, b_2, e_2, c_1Polygon(B, F, E) → poly4, e_3, b_3, f_1Polygon(A, E, F) → poly5, f_2, a_3, e_4Midpoint(F, A) → HMidpoint(F, B) → IMidpoint(A, D) → JMidpoint(B, C) → KMidpoint(A, B) → LMidpoint(D, C) → MCircle(D, ja) → gCircle(A, ja) → hCircle(J, ja) → kLine(J, K) → iIntersect(g, d, 1) → NCircle(K, ja) → pIntersect(k, b, 2) → OIntersect(p, c, 2) → PIntersect(k, b, 1) → QIntersect(p, c, 1) → RLine(O, P) → jLine(Q, R) → lCircle(O, ja) → qCircle(Q, ja) → sIntersect(q, j, 1) → SIntersect(s, l, 1) → TVector(S, N) → uIntersect(h, a, 1) → UVector(T, U) → vCircle(C, ja) → rIntersect(g, b, 2) → VIntersect(r, c, 2) → WCircle(M, ja) → tIntersect(t, d) → Z, A_1Circle(L, ja) → g_1Intersect(g_1, a) → B_1, C_1Line(C_1, A_1) → mLine(B_1, Z) → nCircle(A_1, ja) → h_1Circle(Z, ja) → k_1Intersect(h_1, m, 2) → D_1Intersect(k_1, n, 2) → E_1Vector(D_1, W) → wVector(E_1, V) → u_1If(x(E) < x(D), "c", "d") → TdCircle(H, ja) → p_1Intersect(p_1, a) → F_1, G_1Line(G_1, f) → i_1Line(F_1, i_1) → j_1Circle(G_1, ja) → q_1Circle(F_1, ja) → r_1Intersect(q_1, i_1, 1) → H_1Intersect(r_1, j_1, 1) → I_1Circle(F, ja) → s_1Intersect(s_1, a) → J_1, K_1Intersect(h, b, 1) → L_1Circle(B, ja) → d_2Intersect(d_2, c, 1) → O_1Intersect(s_1, f, 1) → M_1Circle(I, ja) → t_1Intersect(t_1, a) → N_1, P_1Line(P_1, c) → l_1Line(N_1, c) → m_1Circle(N_1, ja) → c_2Circle(P_1, ja) → g_2Intersect(c_2, m_1, 1) → Q_1Intersect(g_2, l_1, 1) → R_1If(x(E) < x(C), Vector[Q_1, M_1], Vector[R_1, M_1]) → n_1If(x(E) < x(C), Vector[R_1, O_1], Vector[Q_1, O_1]) → u_2If(x(E) > x(D), Vector[H_1, M_1], Vector[I_1, M_1]) → w_1If(x(E) > x(D), Vector[I_1, L_1], Vector[H_1, L_1]) → v_1Circle(P, ja) → h_2Circle(R, ja) → k_2Intersect(h_2, j, 2) → S_1Intersect(k_2, l, 2) → T_1Intersect(r, d, 2) → U_1Intersect(d_2, a, 2) → V_1Vector(S_1, U_1) → v_2Vector(T_1, V_1) → w_2Angle(A, D, E) → αAngle(E, B, A) → βAngle(E, F, B) → γAngle(E, C, B) → δAngle(B, A, E) → εAngle(C, B, A) → ζAngle(A, F, E) → ηAngle(A, D, C) → θFractionText(0.5) → text7SelectedIndex(Bahasa) → nnIf(nn ≟ 1, LaTeX["\text{Area of red region = }"], LaTeX["\text{Luas rantau merah = }"]) → Tex1
AI 绘图提示语参考
画一个三角形,动态计算其面积。首先绘制坐标轴并确定三角形的顶点,然后连接顶点形成三角形。接着,通过交点和向量确定关键点,并利用这些点构建多个辅助图形,如正交线、圆和四边形。最后,展示三角形面积的计算过程,包括中点、向量以及辅助图形的运用。
以上提示语为根据原始绘图命令整理而来,仅供参考。