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Investigation: Is SSA a Congruence Shortcut?

Investigation: Is SSA a Congruence Shortcut?
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2016-03-03 05:36
TriangleAngleTrigonometryGeometric Construction
This example demonstrates using GeoGebra dynamic construction to explore whether SSA (two sides and a non-included angle) condition guarantees triangle congruence. It involves core concepts like triangle congruence criteria, trigonometry, and geometric construction. Key GeoGebra commands used include Circle, Point, Segment, Polygon, Rotate, Angle, Ray. Suitable for middle school and above students to understand congruence theorems and geometric proofs.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Circle(A, b) → d
  3. Point(d) → B
  4. Point(c) → C_1
  5. Segment(A, C_1) → e
  6. Segment(A, B) → f
  7. Polygon(C_1, A, B) → poly1, b_1, c_1, a_1
  8. Rotate(A, (-α), B) → A'
  9. Angle(A', B, A) → β
  10. Ray(B, A') → g
  11. Point(g) → C_2
  12. Segment(B, C_2) → h
  13. Segment(C_1, C_2) → i
  14. Angle(B, A, C_1) → γ
  15. Angle(A, C_1, B) → δ