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Similar Triangles with Missing Lengths (Self-Check)

Similar Triangles with Missing Lengths (Self-Check)
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2012-07-25 23:09
TrianglePolygonAngleTransformationGeometric Construction
In collections Ratios and Proportions Ratios and Proportions
This GeoGebra example demonstrates two sets of similar triangles and guides learners to find missing side lengths using proportionality, with an integrated self-check mechanism. Core mathematical concepts include similar triangles, corresponding sides in proportion, scale factor, dilation, and solving for unknown lengths. The construction uses GeoGebra commands such as Polygon to build triangles ABCleft, ABCbottom, ABCright, and DEFbottom; Angle to mark α, β, γ, δ, ε; Segment to draw sides d, e, f, a, b, c, h, i, j, k; Rotate, Ray, and Intersect to generate points E, F, F₁, G, H, I, J, K, R, Q, D, P; and Vector and Translate for transformation-related drawing. Text objects AnswerA, AnswerB, T2, T3, T4 provide answer feedback. Suitable for middle school geometry (grades 7–9) and high school similarity review, ideal for classroom demonstration, independent practice, and self-assessment.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → P, ABCleft, ABCbottom, ABCright
  2. Angle(C, B, A) → α
  3. Angle(A, C, B) → β
  4. Angle(B, A, C) → γ
  5. Segment(E, F) → d
  6. Rotate(F, α, E) → F_1
  7. Angle(F, E, F_1) → δ
  8. Rotate(E, (-β), F) → G
  9. Angle(G, F, E) → ε
  10. Ray(F, G) → e
  11. Ray(E, F_1) → f
  12. Intersect(e, f) → D
  13. Polygon(D, E, F) → Q, a, DEFbottom, b
  14. Polygon(H, I, J, K) → R, h, i, j, k
  15. Vector((0, (c - 7) / 2)) → u
  16. Translate(H, u) → H'
  17. Translate(I, u) → I'
  18. Translate(J, u) → J'
  19. Translate(K, u) → K'
  20. Polygon(H', I', J', K') → R', h', i', j', k'
  21. Vector((0, (g - 7) / 2)) → v
  22. Polygon(L, M, N, O) → S, l, m, n, o
  23. Translate(L, v) → L'
  24. Translate(M, v) → M'
  25. Translate(N, v) → N'
  26. Translate(O, v) → O'
  27. Polygon(L', M', N', O') → S', l', m', n', o'

AI Drawing Prompt Reference

Draw two sets of similar triangles ABCleft, ABCbottom, and ABCright, and DEFbottom. Use angles α, β, γ, and δ to construct the triangles. Generate points E, F, F₁, G, H, I, J, K, R, Q, and D through rotation and translation. Draw segments d, e, f, a, b, c, h, i, j, k to ensure they are proportional. Finally, create new triangles R' and S' through translation to check for similarity.
The prompt above was compiled from the original drawing commands and is for reference only.