探索AAS/SAA全等条件
几何画板及绘图内容加载中,请稍等……
①本范例演示了通过角-角-边(AAS)或角-角-角(SAA)条件判定三角形全等的几何现象;②涉及的核心数学概念包括全等三角形判定定理、角度测量、线段长度比较、动态几何交互;③作图要点提炼自构造摘要,使用了Circle(圆)、Rotate(旋转)、Ray(射线)、Point(点)、Intersect(交点)、DynamicCoordinates(动态坐标)、Angle(角度)、Segment(线段)、If(条件判断)等GeoGebra命令与对象;④适合高中数学学生学习和理解三角形全等判定定理,也可用于几何作图教学演示。
GeoGebra 命令及参数
Circle(A_2, Side3) → c_1Circle(A_2, Side2) → d_1Rotate(A_2, (-Angle1), A_2) → JRotate(G, (-Angle1), A_2) → G'Ray(J, G') → b_1Point(b_1) → InvC_3Intersect(d_1, b_1, 1) → C_3DynamicCoordinates(InvC_3, If[Distance[C_3, InvC_3] < Sticky, x(C_3), x(InvC_3)], If[Distance[C_3, InvC_3] < Sticky, y(C_3), y(InvC_3)]) → C_2''Ray(A_2, G) → a_1Intersect(c_1, a_1, 1) → B_4Point(a_1) → InvB_3DynamicCoordinates(InvB_3, If[Distance[B_4, InvB_3] < Sticky, x(B_4), x(InvB_3)], If[Distance[B_4, InvB_3] < Sticky, y(B_4), y(InvB_3)]) → B_2Circle(B_2, 0.1) → e_1Intersect(e_1, a_1) → K, LRotate(K, Angle2, B_2) → K'Ray(B_2, K') → f_1Circle(B_2, NonIncSide) → g_1Intersect(g_1, f_1) → C_2',Ray(A_3, E) → kPoint(k) → InvB_2Rotate(E, Angle1, A_3) → E'Rotate(A_3, Angle1, A_3) → FRay(F, E') → k'Circle(A_3, WrongSide3) → qIntersect(q, k, 1) → B_5DynamicCoordinates(InvB_2, If[Distance[B_5, InvB_2] < Sticky, x(B_5), x(InvB_2)], If[Distance[B_5, InvB_2] < Sticky, y(B_5), y(InvB_2)]) → B_3Circle(B_3, 0.1) → rIntersect(r, k) → H, IRotate(H, (-Angle2), B_3) → H'Ray(B_3, H') → mPoint(m) → InvC_2Circle(B_3, WrongSide1) → sIntersect(s, m, 1) → C_2DynamicCoordinates(InvC_2, If[Distance[C_2, InvC_2] < Sticky, x(C_2), x(InvC_2)], If[Distance[C_2, InvC_2] < Sticky, y(C_2), y(InvC_2)]) → C_3'Circle(A_3, NonIncSide) → pIntersect(p, k', 1) → C_3''Ray(A_1, A) → aCircle(A_1, Side3) → cIntersect(c, a, 1) → BPoint(a) → InvBDynamicCoordinates(InvB, If[Distance[B, InvB] < Sticky, x(B), x(InvB)], If[Distance[B, InvB] < Sticky, y(B), y(InvB)]) → B_1Rotate(A_1, Angle1, A_1) → C_1Rotate(A, Angle1, A_1) → A'Ray(C_1, A') → a'Circle(A_1, Side2) → dIntersect(d, a', 1) → CPoint(a') → InvCDynamicCoordinates(InvC, If[Distance[C, InvC] < Sticky, x(C), x(InvC)], If[Distance[C, InvC] < Sticky, y(C), y(InvC)]) → C_1'Circle(B_1, NonIncSide) → eAngle(B_1, A_1, C_1') → αSegment(A_1, B_1) → fSegment(A_1, C_1') → gPoint(f) → DRotate(D, (-Angle2), B_1) → D'Ray(B_1, D') → bCircle(B_1, NonIncSide) → hIntersect(h, b, 1) → C_1''Segment(B_1, C_1'') → iAngle(C_1'', B_1, A_1) → βIf(Distance[C_1', C_1''] < 0.2, Polygon[A_1, B, C]) → poly1If(Distance[C_3', C_3''] < 0.2, Polygon[A_3, B_5, C_3'']) → poly2Segment(A_3, C_3'') → lAngle(B_5, A_3, C_3'') → γAngle(C_2, B_3, A_3) → δSegment(A_3, B_3) → nSegment(B_3, C_3') → tAngle(C_3, A_2, B_4) → εAngle(A_2, B_2, C_2') → ζSegment(A_2, B_2) → h_1If(Distance[C_2', C_2''] < 0.2, Polygon[A_2, B_2, C_2'']) → poly3Segment(B_2, C_2') → i_1Segment(C_2'', A_2) → j_1
AI 绘图提示语参考
画两个三角形,展示 AAS 或 SAA 全等条件。首先画一个圆和一条线段,以其中一个顶点为圆心,线段为半径画圆。旋转其中一个角,得到第二个顶点。连接顶点,交点处画圆,再交点处画线段。动态显示交点坐标。重复此过程画第二个三角形,展示全等关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。