平行四边形、矩形与正方形的几何性质与作图演示
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本 GeoGebra 范例动态演示了平行四边形、矩形、菱形和正方形等特殊四边形的几何构造及其核心性质。核心数学概念包括平行四边形的边角关系、面积与周长计算、对角线性质(如垂直与平分)以及相关的圆。作图要点上,该课件通过 GeoGebra 的 Point、Segment、Rotate、Angle、Line、Intersect、OrthogonalLine、Polygon 和 Circle 等几何作图命令,结合参数 a, b, α 和顶点 A, B, C, D 等对象,生动展现了从一般平行四边形向矩形、正方形过渡时几何特征的变化。本工具非常适合中学及大学阶段的几何学习、课堂演示或自主探究。
GeoGebra 命令及参数
Point(Circle[A, a]) → BSegment(A, B) → ABPoint(Circle[A, b]) → DpomocnaSegment(A, Dpomocna) → b'pomocniRotate(Dpomocna, α, A) → DAngle(Dpomocna, A, D) → α_1Segment(A, D) → AD_1Line(D, AB) → laLine(B, AD_1) → lbIntersect(la, lb) → CLine(A, B) → lABOrthogonalLine(D, lAB) → n_aIntersect(n_a, lAB) → ESegment(D, E) → h_aPolygon(A, B, C, D) → Paralelogram, a_0, b_0, c_0, d_0Polygon(A_2, B_2, C_2, D_2) → Pravougaonik, a_2, b_2, c_2, d_2Angle(B_2, A_2, D_2) → αPPolygon(A_3, B_3, C_3, D_3) → Kvadrat, a_3, b_3, c_3, d_3Polygon(A_4, B_4, C_4, D_4) → Romb, a_4, b_4, c_4, d_4Angle(B_3, A_3, D_3) → αKAngle(B_4, A_4, D_4) → αRSegment(D_4, Er_1) → hSegment(A, C) → ACSegment(B, D) → BDIntersect(AC, BD) → OSegment(B_2, D_2) → dpSegment(A_2, C_2) → dp_1Intersect(dp, dp_1) → O_1Segment(D_3, B_3) → dkSegment(A_3, C_3) → dk_1Segment(A_4, C_4) → dr1Segment(B_4, D_4) → dr2Intersect(dr2, dr1) → O_3Intersect(dk_1, dk) → O_2Circle(O_1, A_2) → k_pCircle(O_3, h / 2) → k_rSegment(O_1, B_2) → r_pIntersect(k_r, a_4) → Er_2,Segment(O_3, Er_2) → r_rCircle(O_2, dk / 2) → k_oCircle(O_2, a / 2) → k_uSegment(O_2, B_3) → r_oIntersect(k_u, a_3) → Ek,Segment(O_2, Ek) → r_uOrthogonalLine(D, lb) → n_bIntersect(lb, n_b) → FSegment(D, F) → h_bPoint(lAB) → A_1Point(la) → D_1Polygon(A_1, B_1, C_1, D_1) → P, a_1, b_1, c_1, d_1Segment(D_1, E_0) → ha_0Angle(D, C, B) → γAngle(C, B, A) → βAngle(A, D, C) → δAngle(B_4, O_3, C_4) → αRdSegment(O_3, C_4) → dr1pSegment(B_4, O_3) → dr2pAngle(B_4, A_4, O_3) → αR_1Angle(O_3, A_4, D_4) → αR_2