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SAS Theorem Exercise 3: Proving Triangles Congruent

SAS Theorem Exercise 3: Proving Triangles Congruent
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2016-11-30 22:40
TriangleTransformationGeometric Construction
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This example demonstrates how to prove triangles congruent using the SAS theorem. Key math concepts include triangle congruence and transformational geometry. It uses GeoGebra commands such as Ray, Rotate, Polygon, etc., for geometric construction. Suitable for middle school and above students to learn triangle congruence proof methods.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → f
  2. Rotate(B_1, α, A) → B'
  3. Angle(B_1, A, B') → β
  4. Point(f) → B
  5. Ray(A, B') → g
  6. Point(g) → C
  7. Polygon(A, B, C) → poly1, h, i, j
  8. Segment(A, C) → k
  9. Segment(A, B) → l
  10. Circle(A, (0.2 * Min[k, l])) → c
  11. Intersect(c, f) → F,
  12. Intersect(c, k) → G,
  13. CircleSector(A, F, G) → d
  14. Point(xAxis) → H
  15. Vector(H, I) → u
  16. Translate(A, u) → A'
  17. Translate(C, u) → D'
  18. Segment(A', D') → k'
  19. Translate(A, u) → A'_1
  20. Translate(B, u) → C'
  21. Translate(C, u) → D'_1
  22. Polygon(A'_1, C', D'_1) → poly1', d'_1, a'_1, c'
  23. Segment(D'_1, A'_1) → m
  24. Segment(C', A'_1) → n
  25. Segment(D'_1, C') → p
  26. Circle(A'_1, Radius[c]) → e
  27. Intersect(e, n, 1) → J
  28. Intersect(e, m, 1) → K
  29. CircleSector(A'_1, J, K) → q
  30. Line(L, M) → r
  31. Mirror(A'_1, r) → N
  32. Mirror(C', r) → C''
  33. Mirror(D'_1, r) → O
  34. Polygon(N, C'', O) → poly1'', o, n_1, c''
  35. Mirror(q, r) → q'
  36. Rotate(N, γ, P) → N'
  37. Rotate(C'', γ, P) → C'''
  38. Rotate(O, γ, P) → O'
  39. Polygon(N', C''', O') → poly1''', o', n', c'''
  40. Rotate(q', γ, P) → q''
  41. Segment(N', O') → s
  42. Segment(N', C''') → t
  43. Segment(O', C''') → a