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Does SSA Prove Congruent Triangles?

Does SSA Prove Congruent Triangles?
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2019-02-06 07:33
TriangleAngleGeometric Construction
In collections Triangle Congruence Criteria Visual Representations
This example demonstrates the geometric phenomenon of determining whether triangles are congruent given two sides and a non-included angle (SSA). It involves core mathematical concepts such as triangle congruence criteria. The construction uses GeoGebra commands/objects like Point, Segment, Rotate, Angle, and Line. Suitable for high school mathematics education, exploring SSA conditions in triangle congruence problems.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 5]) → B
  2. Segment(A, B) → f
  3. Point(Circle[B, 3]) → C
  4. Segment(B, C) → g
  5. Point(Circle[D, 5]) → E
  6. Segment(D, E) → h
  7. Point(Circle[E, 3]) → F
  8. Segment(E, F) → i
  9. Rotate(B, (-(30°)), A) → B'
  10. Angle(B', A, B) → α
  11. Rotate(E, (-(30°)), D) → E'
  12. Angle(E', D, E) → β
  13. Line(A, B') → j
  14. Line(D, E') → k
  15. Rotate(E, (-(60°)), E) → E'_1
  16. Rotate(F, (-(85°)), E) → F'
  17. Segment(E'_1, F') → i'
  18. Rotate(B, (-(160°)), B) → B'_1
  19. Rotate(C, (-(155°)), B) → C'
  20. Segment(B'_1, C') → g'
  21. Segment(A, C') → l
  22. Segment(D, F') → m