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Is SSA a Valid Congruence Criterion?

Is SSA a Valid Congruence Criterion?
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2015-12-17 01:50
TriangleCircleAngleVectorGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Unit 5: Triangle Congruence Triangle Congruence Theorems 1
① This example demonstrates whether a triangle is uniquely determined by two sides and a non‑included angle (SSA), showing the ambiguous case and the possible two solutions. ② Core math concepts: triangle congruence criteria, the SSA ambiguous case, relationships between angles and side lengths, and geometric construction verification. ③ Construction highlights: Circle creates the locus of a fixed side length; Point, Segment, Ray, Vector define vertices and vectors; Translate copies elements; Angle measures the given angle; Polygon forms the triangle region. ④ Suitable for high‑school geometry lessons on congruence, teacher demonstrations, and student inquiry.

GeoGebra Commands & Parameters

  1. Circle(B, B_1) → c
  2. Point(c) → A
  3. Point(c) → D
  4. Segment(B, A) → a
  5. Segment(B, D) → b
  6. Segment(D, A) → d
  7. Ray(A, D) → e
  8. Point(e) → E_1
  9. Ray(D, E_1) → f
  10. Point(f) → C
  11. Segment(B, C) → g
  12. Segment(D, C) → h
  13. Vector((0, 0), (0, -3)) → u
  14. Translate(B, u) → F
  15. Translate(A, u) → E
  16. Segment(F, E) → a'
  17. Translate(B, u) → A'_1
  18. Translate(D, u) → H
  19. Segment(A'_1, H) → b'
  20. Translate(D, u) → D'_1
  21. Translate(A, u) → C'_1
  22. Segment(D'_1, C'_1) → d'
  23. Translate(B, u) → A'_2
  24. Translate(C, u) → G
  25. Segment(A'_2, G) → g'
  26. Translate(D, u) → H_1
  27. Translate(C, u) → F'_1
  28. Segment(H_1, F'_1) → h'
  29. Segment(E, G) → i
  30. Segment(A, C) → j
  31. Angle(B, C, A) → α
  32. Angle(F, G, H) → β
  33. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  34. Polygon(F, G, H) → poly2, h_1, f_1, g_1