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ASA Triangle Congruence by Kiley Thergesen

ASA Triangle Congruence by Kiley Thergesen
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2015-12-01 01:59
TriangleAngleGeometric Construction
This example demonstrates the ASA (Angle-Side-Angle) triangle congruence. Key mathematical concepts include triangle congruence and angles. Using GeoGebra commands such as Polygon, Point, Circle, Intersect, etc., it constructs triangles that meet the ASA criteria. Suitable for middle school and above students to learn about triangle congruence.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(c) → D
  3. Circle(A, D) → d
  4. Intersect(d, b, 1) → E
  5. Circle(D, E) → e
  6. Circle(A', c) → f
  7. Circle(A', Radius[d]) → g
  8. Point(f) → B'
  9. Segment(A', B') → h
  10. Intersect(g, h, 1) → H
  11. Circle(H, Radius[e]) → k
  12. Intersect(g, k, 2) → I
  13. Ray(A', I) → i
  14. Point(a) → J
  15. Circle(B, J) → p
  16. Intersect(p, c, 1) → K
  17. Circle(J, K) → q
  18. Circle(B', Radius[p]) → r
  19. Intersect(r, h, 1) → L
  20. Circle(L, Radius[q]) → s
  21. Intersect(r, s, 1) → M
  22. Ray(B', M) → j
  23. Intersect(i, j) → N
  24. Angle(N, A', B') → α
  25. Angle(A', B', N) → β
  26. Angle(A, B, C) → γ
  27. Angle(C, A, B) → δ

AI Drawing Prompt Reference

Draw a triangle ABC with angles A and B having sizes γ and δ, respectively, and the length of side AB known. Then, draw a circle centered at A with radius AB, intersecting the other side of angle A at point D. Draw a circle centered at D with radius AD, intersecting the circle centered at A with radius AB at point E. Connect AE and intersect it with a circle centered at D with radius DE at point F. Draw a circle centered at F with radius FD, intersecting the circle centered at A with radius AB at point G. Connect AG and intersect it with a circle centered at F with radius FG at point H. Connect AH and intersect it with a circle centered at F with radius FH at point I. Connect AI and intersect it with a circle centered at G with radius GI at point J. Connect BJ and intersect it with a circle centered at A with radius AB at point K. Draw a circle centered at K with radius JK, intersecting a circle centered at B with radius BK at point L. Connect BL and intersect it with a circle centered at K with radius KL at point M. Connect KM and intersect it with AI at point N. Measure the size of angle ANB.
The prompt above was compiled from the original drawing commands and is for reference only.