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Are They Congruent?

Are They Congruent?
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2016-10-31 12:13
TriangleVectorTransformation
In collections Elementary Geometry
This example demonstrates how to determine if two triangles are congruent through transformations. Congruence means that one triangle can be transformed into the other by translation, rotation, or reflection. Commands used include point, segment, semicircle, intersect, polygon, random element, mirror, vector, and translate. Suitable for middle and high school students learning about geometric transformations and congruent triangles.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 9]) → B
  2. Segment(A, B) → f
  3. Semicircle(A - (10 * (B - A) / Distance[A, B]), A + (10 * (B - A) / Distance[A, B])) → c
  4. Semicircle(B - (11 * (B - A) / Distance[A, B]), B + (11 * (B - A) / Distance[A, B])) → d
  5. Intersect(c, d, 1) → C
  6. Polygon(B, C, A) → poly1, a, b, c_1
  7. RandomElement(list1) → e
  8. RandomElement(list1) → g
  9. RandomElement(list1) → h
  10. Point(Circle[D, e]) → E
  11. Semicircle(D - ((g * (E - D))) / Distance[D, E], D + ((g * (E - D))) / Distance[D, E]) → k
  12. Semicircle(E + ((h * (D - E))) / Distance[D, E], E - ((h * (D - E))) / Distance[D, E]) → p
  13. Intersect(k, p, 1) → F
  14. Polygon(F, D, E) → poly2, e_1, f_1, d_1
  15. Segment(G, H) → i
  16. Mirror(B, i) → B'
  17. Mirror(C, i) → C'
  18. Mirror(A, i) → A'
  19. Polygon(B', C', A') → poly1', a', b', c'
  20. Vector(I, J) → u
  21. Translate(If[j, poly1', poly1], u) → poly3

AI Drawing Prompt Reference

Draw two congruent triangles ABC and DEF. First, draw line segment f with endpoints A and B. Then, draw semicircles c and d centered at A and B respectively, which intersect at point C. Next, randomly select point D and draw semicircles k and p centered at D, which intersect at point F. Then, draw triangle DEF with vertices D, E, and F. After that, draw vector u and translate triangle DEF along vector u to get the mirrored triangle A'B'C'. Finally, draw line segment i and mirror triangle ABC at point B to get triangle A'B'C', then translate triangle ABC along line segment i to get triangle DEF.
The prompt above was compiled from the original drawing commands and is for reference only.