MathPlotAI Logo MathPlotAI

Congruent Triangles Exercise 2 by Anthony OR 柯志明

Congruent Triangles Exercise 2 by Anthony OR 柯志明
Loading the math board and drawing, please wait…
2013-04-10 18:04
TriangleGeometric Construction
In collections Congruence (Vol 1) Unit 5: Triangle Congruence Naming Congruent Triangles with Reasons Naming Congruent Triangles with Reasons Congruence cases
This example demonstrates how to name congruent triangles and their reasons through moving, rotating, and reflecting. Using GeoGebra commands such as Polygon, Vector, Angle, etc., you can dynamically explore the properties of triangles. Suitable for middle school and above students to learn about congruent triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Vector(P, A) → u
  3. Vector(P, B) → v
  4. Vector(P, C) → w
  5. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_1, b_1
  6. Vector(P_1, A_1) → u_1
  7. Vector(P_1, B_1) → v_1
  8. Vector(P_1, C_1) → w_1
  9. Angle(B, A, C) → α
  10. Angle(A, C, B) → β
  11. Angle(A_1, C_1, B_1) → γ
  12. Angle(B_1, A_1, C_1) → δ
  13. Intersect(Circle[X_0, Side_b], Circle[Y_0, Side_a]) → Z_0, L, ,
  14. Polygon(X_0, Y_0, Z_0) → poly2, z_0, x_0, y_0
  15. Textfield(text13) → Ans1
  16. Textfield(text14) → Ans2
  17. Segment(D, E) → r
  18. Midpoint(Segment[Intersect[Circle[A, r], b], Intersect[Circle[A, r], c]]) → F
  19. Midpoint(Segment[Intersect[Circle[C, r], a], Intersect[Circle[C, r], b]]) → G
  20. Midpoint(Segment[Intersect[Circle[A_1, r], b_1], Intersect[Circle[A_1, r], c_1]]) → H
  21. Midpoint(Segment[Intersect[Circle[C_1, r], a_1], Intersect[Circle[C_1, r], b_1]]) → I
  22. Angle(A_1, B_1, C_1) → ε
  23. Angle(C, B, A) → ζ
  24. Midpoint(Segment[Intersect[Circle[B, r], a], Intersect[Circle[B, r], c]]) → J
  25. Midpoint(Segment[Intersect[Circle[B_1, r], a_1], Intersect[Circle[B_1, r], c_1]]) → K
  26. Rotate(Translate[Mirror[X_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → X_1
  27. Rotate(Translate[Mirror[Y_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → Y_1
  28. Rotate(Translate[Mirror[Z_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → Z_1

AI Drawing Prompt Reference

Draw two congruent triangles ABC and A_1B_1C_1. Construct vectors u, v, w and u_1, v_1, w_1 from points P and P_1, measure angles α, β, γ, δ, construct triangle X_0Y_0Z_0, and find midpoints F, G, H, I for points A, B, C and A_1, B_1, C_1. Perform rotations, translations, and reflections to generate points X_1, Y_1, Z_1.
The prompt above was compiled from the original drawing commands and is for reference only.