相似图形:快速入门
几何画板及绘图内容加载中,请稍等……
这个范例演示了相似图形的基本概念。它涉及相似三角形和比例关系。通过使用GeoGebra命令如Segment, Rotate, Ray, Point等,可以构造相似图形。适合初中和高中学生学习相似三角形和比例关系。
GeoGebra 命令及参数
Segment(A, B) → aRotate(B, (a_{2} * pi / 180), A) → B'Ray(A, B') → fPoint(f) → CSegment(A, C) → bOrthogonalLine(C, b) → rCircle(C, 1) → tIntersect(t, r, 2) → KOrthogonalLine(K, r) → i_1Point(i_1) → WRotate(E, (a_{2} * pi / 180), D) → E'Ray(D, E') → jSegment(D, E) → a'Circle(D, (a' / a * b)) → dIntersect(d, j, 1) → FSegment(D, F) → b'Line(K, b') → k_1Point(k_1) → ULine(K, a') → j_1Point(j_1) → VCircle(B, 1) → sOrthogonalLine(B, a) → qPoint(q) → MIntersect(s, q, 1) → JOrthogonalLine(J, q) → h_1Point(h_1) → PPolygon(A, B, C) → t1, c_{2}, a_1, b_{1}Polygon(D, F, E) → t2, e, d_1, f_1Min({a, a', b, b'}) → gCircle(A, (0.35 * g)) → hIntersect(h, a, 1) → GIntersect(h, b, 1) → HCircleSector(A, G, H) → kLine(A, a') → iDilate(A, If[6 < l ≤ 7, 7 - l, 0], D) → A'Vector(A, A') → uTranslate(k, u) → k'Point(i) → IAngle(I, A, B) → αCircleArc(A, G, H) → pDilate(D, If[1 < l ≤ 2, 2 - l, 0], J) → D'Vector(D, D') → vTranslate(D, v) → D'_{1}Translate(E, v) → E'_{1}Segment(D'_{1}, E'_{1}) → a''Line(J, a') → g_1Point(g_1) → LAngle(P, J, L) → βRotate(D'_{1}, If[1 < l ≤ 2, ((l - 1) * β), β], D'_{1}) → NRotate(E'_{1}, If[1 < l ≤ 2, ((-(l - 1)) * β), (-β)], D'_{1}) → OSegment(N, O) → a'''Dilate(D, If[2 < l ≤ 3, 3 - l, 0], K) → D'_{2}Vector(D, D'_{2}) → wTranslate(D, w) → D'_{3}Translate(E, w) → E'_{2}Point(j_1) → QPoint(i_1) → RAngle(W, K, U) → γRotate(D'_{3}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → SRotate(E'_{2}, If[2 < l ≤ 3, ((l - 2) * γ), γ], D'_{3}) → TTranslate(D, w) → D'_{4}Translate(F, w) → F'Segment(D'_{4}, F') → b''Rotate(D'_{4}, If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → ZRotate(F', If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], K) → F''Segment(Z, F'') → b'''If(o, 7, 4) → c_1Angle(A, C, B) → δIntersect(t, b, 1) → A_1Rotate(A_1, If[4 < l ≤ 5, ((l - 4) * δ), δ], C) → B_1CircleSector(C, A_1, B_1) → e_1Dilate(C, If[6 < l ≤ 7, 7 - l, 0], F) → C'Vector(C, C') → u_1Translate(e_1, u_1) → p_1Line(C, b') → l_1Point(l_1) → C_1Angle(C_1, C, A) → εSegment(F, E) → m_1Segment(B, C) → cOrthogonalLine(B, c) → r_1Circle(B, 1) → s_1Intersect(s_1, r_1, 1) → D_1Dilate(E, If[3 < l ≤ 4, 4 - l, 0], D_1) → E'_{3}Vector(E, E'_{3}) → v_1Translate(F, v_1) → F'_{1}Translate(E, v_1) → E'_{4}Segment(F'_{1}, E'_{4}) → t_1Line(E, c) → f_2Point(f_2) → E_1Angle(F, E, E_1) → ζRotate(F'_{1}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → F_1Rotate(E'_{4}, If[3 < l ≤ 4, ((l - 3) * ζ), ζ], E'_{3}) → G_1Segment(F_1, G_1) → g_2Rotate(p_1, If[6 < l ≤ 7, ((-(l - 6)) * ε), (-ε)], C') → q_1Angle(B, A, C) → ηRotate(G, If[4 < l ≤ 5, ((l - 4) * η), η], A) → G'CircleSector(A, G, G') → d_2CircleArc(C, A_1, B_1) → e_2Rotate(k', If[6 < l ≤ 7, ((-(l - 6)) * α), (-α)], A') → k''Circle(B, (0.35 * g)) → h_2Intersect(h_2, c, 1) → H_1Intersect(h_2, a, 1) → I_1Angle(C, B, A) → θRotate(H_1, If[4 < l ≤ 5, ((l - 4) * θ), θ], B) → J_1CircleSector(B, H_1, J_1) → k_2Line(B, m_1) → n_1Point(n_1) → K_1Angle(K_1, B, C) → λDilate(B, If[6 < l ≤ 7, 7 - l, 0], E) → B'_{1}Vector(B, B'_{1}) → w_1Translate(k_2, w_1) → p_2Rotate(p_2, If[6 < l ≤ 7, ((-(l - 6)) * λ), (-λ)], B'_{1}) → q_2CircleArc(B, H_1, I_1) → r_2
AI 绘图提示语参考
请绘制一个包含相似三角形的图形。首先,构造点A和B,然后旋转点B得到B'。接着,构造射线从A到B',并找到射线上的点C。然后,构造线段AC和过C的垂直线,以及以C为圆心半径为1的圆。圆与垂直线的交点为K,过K的垂直线与垂直线交于W。继续构造点D、E、F等,形成另一个三角形。构造相似比和圆弧,最终得到两个相似图形。确保图形中包含旋转、射线、圆和相似关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。