三角形全等条件
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本范例演示了三角形全等的条件。通过构造三角形及其相关元素,如边长、角度和旋转,学生可以直观地理解全等三角形的判定定理。使用了Segment(线段)、Circle(圆)、Point(点)、Intersect(交点)、Polygon(多边形)、Angle(角)、Rotate(旋转)等GeoGebra命令。适合初中几何学习。
GeoGebra 命令及参数
Segment(A_1, B_1) → a_1Circle(A_1, B_1) → circle1_1Circle(C_1, B_1) → circle1_2Segment(B_1, C_1) → b_1Segment(C_1, A_1) → c_1Point(Circle[E_1, abs(a_1)]) → D_1Circle(D_1, c_1) → circle1_3Circle(E_1, b_1) → circle1_4Intersect(circle1_3, circle1_4, 1) → F_1Segment(D_1, E_1) → d_1Segment(E_1, F_1) → e_1Segment(D_1, F_1) → f_1Polygon(A_1, B_1, C_1) → poly1_1, mc_1, ma_1, mb_1Polygon(D_1, E_1, F_1) → poly1_2, mf_1, md_1, me_1Circle(B_2, A_2) → circle2_1Circle(B_2, C_2) → circle2_2Segment(A_2, B_2) → a_2Segment(B_2, C_2) → b_2Segment(A_2, C_2) → c_2Angle(C_2, B_2, A_2) → α_21Circle(E_2, a_2) → circle2_3Circle(E_2, b_2) → circle2_4Point(circle2_3) → D_2Rotate(D_2, (-α_21), E_2) → E_2'Line(E_2, E_2') → line2'Intersect(circle2_4, line2', 2) → F_2Segment(D_2, E_2) → d_2Segment(E_2, F_2) → e_2Segment(D_2, F_2) → f_2Angle(F_2, E_2, D_2) → α_22Polygon(A_2, B_2, C_2) → poly2_1, mc_2, ma_2, mb_2Polygon(D_2, E_2, F_2) → poly2_2, mf_2, md_2, me_2Segment(B_{34}, C_{34}) → b_{34}Circle(B_{34}, C_{34}) → circle34_1Segment(B_{34}, A_{34}) → a_{34}Segment(C_{34}, A_{34}) → c_{34}Angle(C_{34}, B_{34}, A_{34}) → α_31Angle(B_{34}, C_{34}, A_{34}) → β_31Circle(E_{34}, b_{34}) → circle34_2Point(circle34_2) → F_{34}Rotate(F_{34}, α_31, E_{34}) → F_{34}'Rotate(E_{34}, (-β_31), F_{34}) → E_{34}'Line(E_{34}, F_{34}') → line34_1'Line(F_{34}, E_{34}') → line34_2'Intersect(line34_1', line34_2') → D_{34}Segment(D_{34}, E_{34}) → d_{34}Segment(E_{34}, F_{34}) → e_{34}Segment(D_{34}, F_{34}) → f_{34}Angle(F_{34}, E_{34}, D_{34}) → α_32Angle(D_{34}, F_{34}, E_{34}) → β_32Polygon(A_{34}, B_{34}, C_{34}) → poly34_1, ma_3, mb_3, mc_3Polygon(D_{34}, E_{34}, F_{34}) → poly34_2, md_3, me_3, mf_3Angle(C_{34}, A_{34}, B_{34}) → β_41Angle(F_{34}, D_{34}, E_{34}) → β_42Segment(A_5, C_5) → c_5OrthogonalLine(C_5, c_5) → line5_1'Point(line5_1') → B_5Segment(A_5, B_5) → a_5Segment(B_5, C_5) → b_5Circle(D_5, c_5) → circle5_1Point(circle5_1) → F_5Segment(D_5, F_5) → f_5OrthogonalLine(F_5, f_5) → line5_2'Circle(D_5, a_5) → circle5_2Intersect(circle5_2, line5_2', 1) → E_5Segment(D_5, E_5) → d_5Segment(E_5, F_5) → e_5Angle(A_5, C_5, B_5) → α_51Angle(D_5, F_5, E_5) → α_52Polygon(A_5, B_5, C_5) → poly5_1, mc_5, ma_5, mb_5Polygon(D_5, E_5, F_5) → poly5_2, mf_5, md_5, me_5Segment(A_6, B_6) → a_6Circle(B_6, A_6) → circle6_1Circle(A_6, C_6) → circle6_2Segment(B_6, C_6) → b_6Segment(A_6, C_6) → c_6Circle(D_6, a_6) → circle6_3Point(circle6_3) → E_6Circle(D_6, c_6) → circle6_4Angle(C_6, B_6, A_6) → α_61Rotate(D_6, (-α_61), E_6) → F_6'Line(E_6, F_6') → line6'Intersect(circle6_4, line6', 1) → F_6Segment(D_6, E_6) → d_6Segment(E_6, F_6) → e_6Segment(D_6, F_6) → f_6Angle(F_6, E_6, D_6) → α_62Polygon(A_6, B_6, C_6) → poly6_1, mc_6, ma_6, mb_6Polygon(D_6, E_6, F_6) → poly6_2, mf_6, md_6, me_6Segment(A_7, B_7) → a_7Segment(B_7, C_7) → b_7Segment(A_7, C_7) → c_7Segment(D_7, E_7) → d_7Angle(C_7, A_7, B_7) → α_71Angle(A_7, B_7, C_7) → β_71Angle(B_7, C_7, A_7) → γ_71Rotate(E_7, (-α_71), D_7) → F_71'Rotate(D_7, β_71, E_7) → F_72'Line(D_7, F_71') → line7_1'Line(E_7, F_72') → line7_2'Intersect(line7_1', line7_2') → F_7Segment(D_7, F_7) → e_7Segment(E_7, F_7) → f_7Angle(F_7, D_7, E_7) → α_72Angle(D_7, E_7, F_7) → β_72Angle(E_7, F_7, D_7) → γ_72Polygon(A_7, B_7, C_7) → poly7_1, mc_7, ma_7, mb_7Polygon(D_7, E_7, F_7) → poly7_2, mf_7, md_7, me_7
AI 绘图提示语参考
画两个三角形,分别标记三个顶点和三条边,用圆表示边长,用角度符号表示三个内角,通过旋转和相交操作展示三角形全等的条件,包括边边边、边角边和角边角三种情况,并用不同颜色区分两个三角形,以便观察全等关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。