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SAS Theorem Exercise 1B: Proving Triangles Congruent

SAS Theorem Exercise 1B: Proving Triangles Congruent
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2019-07-03 20:36
TriangleTransformationGeometric Construction
This example demonstrates how to use the SAS theorem to prove triangle congruence. Key mathematical concepts include triangle congruence and transformational geometry. It uses GeoGebra commands such as Ray, Rotate, Polygon, Segment, etc., for geometric construction. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Ray(A, W) → f
  2. Rotate(W, α, A) → B'
  3. Angle(W, A, B') → β
  4. Point(f) → B
  5. Ray(A, B') → g
  6. Point(g) → C
  7. Polygon(A, B, C) → poly1, h, i, j
  8. Segment(A, C) → k
  9. Segment(A, B) → l
  10. Circle(A, (0.2 * Min[k, l])) → h_5
  11. Intersect(h_5, f) → F,
  12. Intersect(h_5, k) → G,
  13. CircleSector(A, F, G) → d
  14. Point(xAxis) → H
  15. Vector((a, b)) → u
  16. Translate(A, u) → A'
  17. Translate(C, u) → C'
  18. Segment(A', C') → k'
  19. Translate(A, u) → R_1
  20. Circle(R_1, Radius[h_5]) → e
  21. Rotate(A, γ, A) → R_2
  22. Rotate(B, γ, A) → K_1
  23. Rotate(C, γ, A) → K
  24. Polygon(R_2, K_1, K) → poly1'_1, c'_1, a'_2, b'_1
  25. Rotate(d, γ, A) → d'
  26. Segment(A, K_1) → m
  27. Segment(A, K) → n
  28. Segment(K_1, K) → p

AI Drawing Prompt Reference

Draw a triangle to demonstrate triangle congruence using the SAS theorem. Start by drawing a ray, then rotate it around a point to form an angle. Use the two sides of this angle as the base and height to construct a triangle. Next, draw a circle with one side as the radius, intersecting the ray and the other side to get two points. Connect these points to the triangle's vertex and draw another circle with the same radius. Finally, rotate the triangle around the vertex by a certain angle and draw the rotated triangle and a sector.
The prompt above was compiled from the original drawing commands and is for reference only.