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Exploring HL Theorem

Exploring HL Theorem
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2012-02-27 08:07
TriangleAngleGeometric Construction
In collections Similarity and Congruence Year 8 Pedagogies in Practice
This example demonstrates whether HL guarantees triangle congruence by constructing triangles and measuring their sides and angles. Core math concepts include triangle congruence criteria, HL theorem, angle measurement, side calculation. Construction involves commands/objects like Rotate, Ray, Circle, Intersect, Segment, Point, Angle, Polygon from GeoGebra. Suitable for high school students learning triangle congruence criteria.

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