30°-60°直角三角形边长关系
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①本范例演示30°-60°直角三角形三边长度比例关系;②涉及核心概念:特殊三角形性质、三角函数、几何作图;③构造要点:使用Point, Segment, Circle, Midpoint, Intersect, Polygon, Angle, PolyLine等命令绘制并分析三角形及内切圆;④适合初中及以上学生学习特殊三角形性质及几何作图。
GeoGebra 命令及参数
Point(Circle[A, a]) → B_2Segment(A, B_2) → bCircle(A, B_2) → cCircle(B_2, A) → dMidpoint(b) → BIntersect(c, d) → C, E, ,Segment(C, A) → eSegment(C, B) → fSegment(C, B_2) → gPolygon(C, B, A) → poly1, a_1, d_1, c_1Polygon(C, B_2, B) → poly2, c_2, d_2, b_1Angle(C, B, A) → αAngle(B, A, C) → βAngle(A, C, B) → γMidpoint(e) → FMidpoint(f) → GSegment(A, B) → h_1Midpoint(h_1) → HMidpoint(H, B) → IMidpoint(I, H) → JPolyLine(F, J, G) → iPoint(i) → KMidpoint(F, J) → LMidpoint(J, G) → MIntersect(xAxis, yAxis) → OPoint(Circle[O, h]) → PSegment(O, P) → lCircle(O, P) → pCircle(P, O) → qIntersect(p, q, 1) → QMidpoint(l) → RSegment(O, Q) → mSegment(R, Q) → nSegment(O, R) → rPolygon(O, R, Q) → poly3, q_1, o, r_1Midpoint(m) → SMidpoint(l) → TMidpoint(n) → UMidpoint(O, R) → A_1Midpoint(A_1, R) → B_1Midpoint(B_1, A_1) → C_1PolyLine(U, C_1, S) → sPoint(s) → D_1Midpoint(S, C_1) → E_1Midpoint(C_1, U) → VPolygon(Q, O, R) → poly4, r_2, q_2, o_1Angle(R, O, Q) → δAngle(O, Q, R) → εAngle(Q, R, O) → ζ