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HL Postulate for Right Triangle Congruence

HL Postulate for Right Triangle Congruence
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2019-02-06 08:35
TriangleCircleGeometric Construction
In collections Triangle Congruence Criteria Visual Representations
This example demonstrates how to prove right triangles congruent using the HL postulate. It involves core concepts like right triangle congruence, HL criteria, and properties of circles. Constructed with GeoGebra commands and objects such as Point, Segment, Rotate, Angle, Circle, Line, Intersect, Polygon, and If. Suitable for high school geometry instruction and understanding geometric proof methods.

GeoGebra Commands & Parameters

  1. Point(Circle[A, AB]) → B
  2. Segment(A, B) → j
  3. Rotate(A, (-β), B) → A'
  4. Angle(A', B, A) → γ
  5. Circle(A, CA) → c
  6. Line(B, A') → i
  7. Intersect(c, i, 2) → C
  8. Polygon(A, B, C) → poly1, c_1, a, b
  9. Point(Circle[D, n]) → E
  10. Segment(D, E) → f
  11. Rotate(E, p°, D) → E'
  12. Angle(E, D, E') → α
  13. Line(D, E') → h
  14. Circle(E, o) → d
  15. Intersect(d, h) → F_1, F
  16. Polygon(D, F, E) → poly2, e_1, d_1, g_1
  17. Angle(F, E, D) → δ
  18. Angle(E, F, D) → ε
  19. Segment(F, D) → l
  20. Segment(A, B) → m
  21. Segment(D, E) → q
  22. Segment(C, A) → r
  23. Segment(C, A) → s
  24. Segment(F, E) → t
  25. Segment(A, B) → f_1
  26. Angle(A, B, C) → ζ
  27. Angle(E, D, F) → η
  28. Angle(B, A, C) → θ
  29. Angle(B, C, A) → ι
  30. Angle(B, C, A) → κ
  31. Angle(B, A, C) → λ
  32. Segment(C, B) → g
  33. Segment(F, D) → h_1
  34. Segment(C, B) → i_1
  35. Segment(E, D) → j_1
  36. Angle(B, C, A) → μ
  37. Angle(B, A, C) → ν
  38. If(AB ≟ round((Distance[F, D] * 10)) / 10 ∧ CA ≟ Distance[F, E], δ, μ) → AngleBlue
  39. If(AB ≟ round((Distance[F, D] * 10)) / 10 ∧ CA ≟ Distance[F, E], ε, Angle[B, A, C]) → AngleGreen