探索截线与平行线形成的角对性质

几何画板及绘图内容加载中，请稍等……

2016-05-10 04:19

角解析几何几何作图

①本范例演示截线与平行线相交形成的同位角、内错角、同旁内角等特殊角对；②涉及平行线性质、角平分线定理、角度关系等核心概念；③通过 GeoGebra 命令 Line（线）、Ray（射线）、Intersect（交点）、Point（点）、Angle（角度）、AttachCopyToView（视图复制）等完成作图；④适合初中及以上数学教学，用于直观理解几何定理和性质。

GeoGebra 命令及参数

Line(A, B) → f
Line(C, f) → g
Ray(C, D) → h
Intersect(f, h) → E
Point(g) → F
Point(g) → G
Angle(C, E, B) → α
Ray(B, G) → i
AttachCopyToView(PolyLine[(1.140000000000001, 3.859999999999999), (1.080000000000001, 3.839999999999999), (0.960000000000001, 3.839999999999999), (0.8200000000000008, 3.839999999999999), (0.7600000000000009, 3.819999999999999), (0.6800000000000008, 3.819999999999999), (NaN, NaN), (1.200000000000001, 3.799999999999999), (1.200000000000001, 3.6799999999999993), (1.180000000000001, 3.559999999999999), (1.160000000000001, 3.439999999999999), (1.160000000000001, 3.319999999999999), (NaN, NaN), (3.820000000000002, 1.9199999999999984), (4.040000000000002, 1.8999999999999984), (4.140000000000002, 1.8799999999999983), (4.220000000000002, 1.8799999999999983), (NaN, NaN), (4.240000000000002, 1.8999999999999984), (4.240000000000002, 1.6799999999999984), (4.240000000000002, 1.5999999999999983), (4.220000000000002, 1.5199999999999982), (4.200000000000002, 1.4399999999999982), (4.180000000000002, 1.2999999999999983), (NaN, NaN), (-2.3600000000000003, 1.5399999999999983), (-2.4400000000000004, 1.5199999999999982), (-2.5800000000000005, 1.5199999999999982), (-2.6800000000000006, 1.5199999999999982), (-2.8200000000000003, 1.5199999999999982), (-2.9000000000000004, 1.5399999999999983), (NaN, NaN), (-2.3800000000000003, 1.5599999999999983), (-2.3800000000000003, 1.4799999999999982), (-2.3800000000000003, 1.3999999999999981), (-2.3800000000000003, 1.2999999999999983), (-2.3800000000000003, 1.2199999999999982), (-2.3800000000000003, 1.1399999999999981), (-2.3800000000000003, 1.059999999999998), (-2.3800000000000003, 0.9799999999999981), (NaN, NaN), (0.1000000000000006, -0.7400000000000025), (-0.1599999999999995, -0.7400000000000025), (-0.29999999999999954, -0.7600000000000026), (-0.37999999999999956, -0.7800000000000026), (-0.4599999999999996, -0.7800000000000026), (-0.5399999999999996, -0.7800000000000026), (NaN, NaN), (0.14000000000000062, -0.7800000000000026), (0.14000000000000062, -0.9000000000000026), (0.14000000000000062, -1.1200000000000028), (0.14000000000000062, -1.2200000000000026), (NaN, NaN), (3.940000000000002, 6.1), (4.040000000000002, 6.12), (4.140000000000002, 6.12), (4.240000000000002, 6.12), (4.3400000000000025, 6.12), (4.420000000000003, 6.12), (4.500000000000003, 6.1), (4.560000000000002, 6.08), (NaN, NaN), (4.580000000000002, 6.04), (4.580000000000002, 5.8), (4.560000000000002, 5.62), (4.540000000000002, 5.54), (NaN, NaN), (7.160000000000003, 4.14), (7.2600000000000025, 4.14), (7.440000000000003, 4.14), (7.620000000000003, 4.119999999999999), (7.780000000000003, 4.119999999999999), (7.700000000000003, 4.119999999999999), (7.620000000000003, 4.119999999999999), (7.520000000000003, 4.119999999999999), (7.440000000000003, 4.119999999999999), (NaN, NaN), (7.780000000000003, 4.079999999999999), (7.780000000000003, 3.959999999999999), (7.780000000000003, 3.859999999999999), (7.780000000000003, 3.779999999999999), (7.780000000000003, 3.579999999999999), (7.780000000000003, 3.439999999999999), true], 1, (-4.300000000000001, -2.600000000000003), (9.660000000000004, 6.3), (0, 445), (698, 0)) → stroke1
Point(f) → H
Point(g) → I
Point(i) → J

AI 绘图提示语参考

画两条平行线f和g，然后画一条穿过点C并交于f于E的射线h。接着画一条从g上点F和G分别向B点的直线。在点C、E和B之间画出角α。最后画一条从B点出发经过G点的射线i。

以上提示语为根据原始绘图命令整理而来，仅供参考。