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Exploring SSA for Triangle Congruence by jroe

Exploring SSA for Triangle Congruence by jroe
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2012-02-27 08:04
TriangleAngleGeometric Construction
In collections Similarity and Congruence Year 8 Pedagogies in Practice
This example explores whether SSA (two sides and the included angle) guarantees that two triangles are congruent. Key mathematical concepts include conditions for triangle congruence. The construction uses GeoGebra commands such as Rotate, Ray, Circle, etc. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Rotate(A_1, -Angle_B, B) → A'
  2. Ray(B, A') → a
  3. Ray(B, A_1) → b
  4. Circle(B, LengthAB) → c
  5. Intersect(c, b, 1) → A
  6. Segment(A, B) → d
  7. Point(Circle[A, LengthAC]) → C_1
  8. Segment(A, C_1) → e
  9. Rotate(A, Angle_B, B) → A'_1
  10. Angle(A, B, A'_1) → α
  11. Ray(B, A'_1) → f
  12. Point(f) → C
  13. Segment(B, C) → g
  14. Segment(C, C_1) → h
  15. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  16. Angle(C, A, B) → β
  17. Angle(B, C, A) → γ
  18. Segment(C, B) → i

AI Drawing Prompt Reference

Draw a triangle ABC with given lengths of sides AB and BC, and the included angle B. Start by drawing side AB, then draw a circle with center B and radius AB, and draw a perpendicular line from A to intersect the circle at point C1. Next, draw a circle with center B and radius BC, and draw a perpendicular line from C1 to intersect the circle at point C. Finally, connect AC and BC to form triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.