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HL Congruence Theorem Demo

HL Congruence Theorem Demo
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2016-10-03 10:17
TriangleAngleGeometric Construction
This example dynamically demonstrates the HL Congruence Theorem, illustrating that two right triangles are congruent if the hypotenuse and one leg are equal. It covers core concepts like triangle congruence criteria, properties of right triangles, and the SSS congruence theorem. Construction involves GeoGebra commands: Segment, Line, OrthogonalLine, Circle, Intersect, Angle. Suitable for high school mathematics education to visually explain the application of the HL theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, D) → g
  3. Line(F, G) → h
  4. Line(H, I) → i
  5. OrthogonalLine(F, h) → j
  6. OrthogonalLine(H, i) → k
  7. Circle(F, Segment[B, A]) → c
  8. Circle(H, Segment[A, B]) → d
  9. Intersect(c, h, 2) → K
  10. Circle(K, Segment[C, D]) → e
  11. Intersect(d, i, 2) → L
  12. Circle(L, Segment[D, C]) → p
  13. Intersect(e, j, 2) → M
  14. Segment(M, K) → l
  15. Intersect(e, k, 2) → N
  16. Segment(N, H) → n
  17. Segment(H, L) → q
  18. Segment(K, F) → r
  19. Segment(F, M) → s
  20. Segment(H, N) → t
  21. Circle(L, Segment[D, C]) → c_1
  22. Intersect(c_1, t, 1) → O
  23. Segment(L, O) → a
  24. Segment(O, H) → b
  25. Angle(L, H, O) → α
  26. Angle(K, F, M) → β