七巧板中的角
几何画板及绘图内容加载中,请稍等……
所属专题
MateTangram
本范例通过七巧板的各个部件探索角的度量。涉及的核心数学概念包括几何学、等腰三角形、平行四边形、直角三角形、正方形等。使用了Polygon、Segment、Midpoint、Line、Intersect、Rotate、InteriorAngles等GeoGebra命令。适合小学高年级至初中学生学习几何图形和角的相关知识。
GeoGebra 命令及参数
Polygon(A, B, 4) → poli1, frame3, frame4, frame1, frame2, C, DSegment(A, C) → frame12Midpoint(D, C) → EMidpoint(D, A) → FSegment(F, E) → frame5Midpoint(A, C) → GSegment(B, G) → frame9Midpoint(F, E) → HMidpoint(G, C) → ISegment(H, I) → frame7Segment(G, H) → frame8Line(F, frame8) → jIntersect(j, frame12) → JSegment(F, J) → frame11Polygon(A, G, B) → poli2, b_1, a_1, g_1Rotate(O + (a_1, 0), Angle[B - G] + Angle[O - N] - Angle[G - A], O) → PPolygon(N, O, P) → poli4, p, n, oPolygon(B, G, C) → poli3, c_1, b_2, g_2Rotate(L + (b_2, 0), Angle[C - G] + Angle[L - K] - Angle[G - B], L) → MPolygon(K, L, M) → poli5, m, k_1, lPolygon(H, E, C, I) → poli6, h_1, e_1, c_2, i_1Rotate(R + (e_1, 0), Angle[C - E] + Angle[R - Q] - Angle[E - H], R) → SRotate(S + (c_2, 0), Angle[I - C] + Angle[S - R] - Angle[C - E], S) → TPolygon(Q, R, S, T) → poli7, q, r, s, tPolygon(H, G, I) → poli8, i_2, h_2, g_3Rotate(V + (h_2, 0), Angle[I - G] + Angle[V - U] - Angle[G - H], V) → WPolygon(U, V, W) → poli9, w, u, vPolygon(F, H, G, J) → poli10, f_1, h_3, g_4, j_1Rotate(A_1 + (h_3, 0), Angle[G - H] + Angle[A_1 - Z] - Angle[H - F], A_1) → B_1Rotate(B_1 + (g_4, 0), Angle[J - G] + Angle[B_1 - A_1] - Angle[G - H], B_1) → C_1Polygon(Z, A_1, B_1, C_1) → poli11, z, a_2, b_3, c_3Polygon(F, J, A) → poli12, a_3, f_2, j_2Rotate(E_1 + (f_2, 0), Angle[A - J] + Angle[E_1 - D_1] - Angle[J - F], E_1) → F_1Polygon(D_1, E_1, F_1) → poli13, f_3, d_1, e_2Polygon(F, D, E) → poli14, e_3, f_4, d_2Rotate(H_1 + (f_4, 0), Angle[E - D] + Angle[H_1 - G_1] - Angle[D - F], H_1) → I_1Polygon(G_1, H_1, I_1) → poli15, i_3, g_5, h_4InteriorAngles(poli7) → parA, parB, parC, parDInteriorAngles(poli11) → quaA, quaB, quaC, quaDInteriorAngles(poli5) → triGA, triGB, triGCInteriorAngles(poli4) → triVA, triVB, triVCInteriorAngles(poli15) → triAA, triAB, triACInteriorAngles(poli9) → triRA, triRB, triRCInteriorAngles(poli13) → triPUC, triPUA, triPUB
AI 绘图提示语参考
在同一平面绘制一幅由若干多边形拼合的“探角”图形:先给出一组以同一顶点为基础的三角形与四边形构成的初始轮廓,然后取若干边的中点,把相应中点连成线段以形成内部分割。以若干已知点为中心进行多次旋转,把若干小三角形或四边形复制并定向到不同位置,拼出连续的多边形区域。最后得到多个三角形、四边形与一个较大的四边形区域,并在这些多边形内部标注其内角测量值,用于比较各角度大小。
以上提示语为根据原始绘图命令整理而来,仅供参考。