动态演示四边形面积变化
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所属专题
CCSS High School: Geometry (Congruence) Volume 2
CCSS High School: Geometry (Congruence) Volume 2
CCSS High School: Geometry (Congruence) Volume 2
这个范例演示了四边形面积的变化。核心数学概念包括四边形、面积计算和逻辑推理。通过使用GeoGebra命令如Segment、Circle、Line、Intersect等,构建了一个动态的四边形模型。适合初中及以上学生学习几何变换和面积计算。
GeoGebra 命令及参数
Segment(A, D) → fCircle(C, f) → eLine(C, D) → mIntersect(e, m) → H, ICircleArc(C, I, H) → pPoint(p) → BLine(D, B) → g_1Segment(B, D) → nDilate(A, If[0 < a ≤ 1, 1 - a, 0], D) → A'Segment(A, A') → sLine(C, s) → cSegment(D, C) → gMidpoint(g) → NSegment(C, B) → hSegment(B, A) → iMidpoint(i) → MSegment(N, M) → jSegment(A, C) → kIntersect(k, n) → LLine(B, f) → lLine(A, h) → qIntersect(l, q) → KSegment(L, K) → rSlope(j) → m_1Slope(r) → m_2Dilate(D, If[1 < a ≤ 2, 2 - a, 0], N) → B'Segment(D, B') → tDilate(N, If[2 < a ≤ 3, 3 - a, 0], C) → F'Segment(N, F') → bRotate(D, If[3 < a ≤ 4, ((a - 3) * π), π], N) → B'_1Rotate(B', If[3 < a ≤ 4, ((a - 3) * π), π], N) → B''Intersect(g_1, c) → M_1Angle(M_1, C, B) → αSegment(B'_1, B'') → t'Dilate(D, If[4 < a ≤ 5, 5 - a, 0], C) → B'_2Vector(D, B'_2) → uTranslate(A, u) → A'_1Translate(A', u) → A''Segment(A'_1, A'') → s'Rotate(A'_1, If[5 < a ≤ 6, ((a - 5) * α), α], C) → K_1Rotate(A'', If[5 < a ≤ 6, ((a - 5) * α), α], C) → A'''Segment(K_1, A''') → s''Dilate(A, If[6 < a ≤ 7, 7 - a, 0], M) → A'_2Segment(A, A'_2) → dDilate(M, If[7 < a ≤ 8, 8 - a, 0], B) → E'Segment(M, E') → f_1Rotate(A, If[8 < a ≤ 9, ((a - 8) * π), π], M) → A'_3Rotate(A'_2, If[8 < a ≤ 9, ((a - 8) * π), π], M) → L_1Segment(A'_3, L_1) → d'Polygon(A, D, C, B) → poly1, a_1, b_1, c_1, d_1Dilate(N, If[9 < a ≤ 10, 10 - a, 0], M) → F'_1Segment(N, F'_1) → h_1Circle(C, 5) → e_1Intersect(e_1, m, 1) → N_1Ray(C, N_1) → i_1Intersect(m, q) → OSegment(D, O) → j_1Segment(O, N) → k_1Min(j_1, k_1) → oCircle(C, (0.25 * o)) → p_1Intersect(p_1, i_1, 1) → PIntersect(p_1, s'', 1) → QAngle(Q, C, P) → βRotate(Q, If[10 < a ≤ 11, ((a - 10) * β), β], C) → Q'CircleSector(C, Q, Q') → q_1Dilate(A, If[11 < a ≤ 12, 12 - a, 0], K) → A'_4Segment(A, A'_4) → l_1Dilate(C, If[12 < a ≤ 13, 13 - a, 0], O) → C'Vector(C, C') → vTranslate(q_1, v) → r_1Intersect(m, l) → RLine(D, A) → n_1Circle(D, 5) → s_1Intersect(s_1, n_1, 1) → SRay(D, S) → t_1Segment(N, R) → f_2Segment(R, C) → g_2Min(f_2, g_2) → wCircle(D, (0.25 * w)) → c_2Intersect(c_2, t_1, 1) → UIntersect(c_2, m) → T, VAngle(T, D, U) → γRotate(T, If[13 < a ≤ 14, ((a - 13) * γ), γ], D) → T'CircleSector(D, T, T') → d_2Dilate(D, If[15 < a ≤ 16, 16 - a, 0], R) → B'_3Vector(D, B'_3) → u_1Translate(d_2, u_1) → e_2Dilate(B, If[14 < a ≤ 15, 15 - a, 0], K) → D'Segment(B, D') → h_2Intersect(m, r) → WCircle(W, (0.6 * Distance[W, N])) → k_2Dilate(A, If[16 < a ≤ 17, 17 - a, 0], L) → A'_5Dilate(B, If[16 < a ≤ 17, 17 - a, 0], L) → D'_1Segment(A, A'_5) → i_2Segment(B, D'_1) → j_2Line(K, W) → l_2Intersect(k_2, l_2) → Z, A_1Intersect(k_2, m) → B_1, C_1Dilate(L, If[17 < a ≤ 18, 18 - a, 0], D) → G'Dilate(L, If[17 < a ≤ 18, 18 - a, 0], C) → G'_1Segment(L, G') → n_2Segment(L, G'_1) → p_2Dilate(L, If[18 < a ≤ 19, 19 - a, 0], K) → G'_2Segment(L, G'_2) → q_2Angle(A_1, W, B_1) → δRotate(A_1, If[19 < a ≤ 20, ((a - 19) * δ), δ], W) → D_1CircleSector(W, A_1, D_1) → r_2Dilate(W, If[20 < a ≤ 21, 21 - a, 0], N) → W'Vector(W, W') → v_1Translate(r_2, v_1) → s_2
AI 绘图提示语参考
绘制一个四边形,并通过调整参数a来改变四边形的形状和大小。首先,创建点A、B、C、D,然后通过这些点构造四边形。接着,使用圆、线段和交点命令创建辅助线和点,如点B、点N等。通过缩放、旋转和平移命令,动态改变四边形的形状和大小,观察面积的变化。
以上提示语为根据原始绘图命令整理而来,仅供参考。