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SAS Triangle Congruence Exploration by Julian Ornelas

SAS Triangle Congruence Exploration by Julian Ornelas
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2017-10-23 06:28
TriangleAngleGeometric Construction
In collections D.G. 4.4 & 4.5: Triangle Congruence Shortcuts
This applet helps students explore triangle congruence using the Side-Angle-Side (SAS) criterion. It demonstrates constructing triangles given two sides and the included angle, and dynamically adjusting these elements to observe changes. Commands used include Ray, Angle, Circle, Point, Intersect, Polygon, and Segment. Suitable for middle school and above students learning about triangle congruence.

GeoGebra Commands & Parameters

  1. Ray(B, C) → a
  2. Ray(B, A) → b
  3. Angle(A, B, C) → α
  4. Circle(B', Segment[C, B]) → c
  5. Circle(B', Segment[A, B]) → d
  6. Point(c) → C'
  7. Circle(C', Segment[A, C]) → e
  8. Intersect(d, e, 2) → A'
  9. Ray(B', C') → f
  10. Ray(B', A') → g
  11. Polygon(B, C, A) → poly1, c_1, a_1, b_1
  12. Segment(B', C') → h
  13. Segment(B', A') → i
  14. Segment(C', C'') → j
  15. Angle(B, C, A) → β
  16. Angle(C, A, B) → γ
  17. Angle(A', B', C') → δ
  18. Angle(B', C', C'') → ε
  19. Segment(C'', A') → k
  20. Circle(C'', 1) → p
  21. Circle(A', 1) → q
  22. Segment(C'', B') → l
  23. Intersect(p, l, 1) → E
  24. Segment(C'', E) → r
  25. Angle(C', C'', B') → ζ

AI Drawing Prompt Reference

Draw a triangle ABC with given lengths of AB and AC and the included angle ∠BAC. First, draw rays BA and BC, then construct ∠BAC. Next, draw circles with center B and radii AB and AC, and find their intersection point A'. Connect BA' and BC', and draw triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.