Are All Equilateral Triangles Congruent?

Are All Equilateral Triangles Congruent?
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2016-02-11 00:25
This example demonstrates the properties and congruence of equilateral triangles. Key mathematical concepts include the definition of an equilateral triangle and the criteria for congruent triangles. Using GeoGebra commands such as Segment (line segment), Circle (circle), Intersect (intersection), and Polygon (polygon), equilateral triangles are constructed and their congruence is verified. Suitable for middle school and above students to learn about geometric constructions and the concept of congruent triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(A, B) → c
  3. Circle(B, A) → d
  4. Intersect(c, d, 1) → C
  5. Polygon(A, B, C) → poly1, c_1, a_1, b
  6. Segment(A_1, B_1) → a_2
  7. Circle(A_1, B_1) → c_2
  8. Circle(B_1, A_1) → d_1
  9. Intersect(c_2, d_1, 1) → C_1
  10. Polygon(A_1, B_1, C_1) → poly1_1, c_3, a_3, b_1