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Girl in the Mirror by GeoGebra Materials Team

Girl in the Mirror by GeoGebra Materials Team
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2014-05-09 15:36
TriangleAngleGeometric Construction
This worksheet explores how large a mirror needs to be to see your full body. It involves the concept of similar triangles. GeoGebra commands used include Point, Intersect, Segment, OrthogonalLine, Line, Mirror, Angle, Polygon. Suitable for high school geometry and trigonometry lessons.

GeoGebra Commands & Parameters

  1. Point(yAxis) → F
  2. Intersect(xAxis, yAxis) → B_2
  3. Segment(B_2, F) → b
  4. Intersect(b, g) → A
  5. OrthogonalLine(L, b) → i
  6. Intersect(b, i) → B
  7. OrthogonalLine(C, b) → e
  8. Point(e) → I
  9. Point(e) → J
  10. Segment(J, I) → h
  11. Point(h) → H
  12. Intersect(c, i) → M
  13. Line(B_1, B_2) → d
  14. OrthogonalLine(B_1, d) → f
  15. Mirror(pic1, b) → pic2
  16. Mirror(H, b) → D
  17. OrthogonalLine(E, b) → a
  18. Intersect(a, c) → G
  19. Intersect(g, c) → K
  20. Mirror(M, b) → N
  21. Mirror(K, b) → O
  22. Segment(G, O) → j
  23. Segment(G, N) → k
  24. Intersect(b, j) → A'
  25. Intersect(b, k) → B'
  26. Angle(B', G, A') → α
  27. Segment(A', B') → l
  28. Segment(G, B') → p
  29. Segment(B', M) → q
  30. OrthogonalLine(B', b) → r
  31. Point(r) → P
  32. Angle(M, B', B) → β
  33. Angle(A', B', G) → γ
  34. Intersect(j, b) → Q
  35. Segment(G, Q) → a1
  36. Segment(K, Q) → b1
  37. OrthogonalLine(G, b) → c1
  38. Intersect(g, j) → R
  39. OrthogonalLine(R, c1) → d1
  40. Point(b) → U
  41. Intersect(b, d) → V
  42. Polygon(U, S, T, V) → poly1, u_1, s_1, t_1, v_1

AI Drawing Prompt Reference

Draw a mirror with its bottom intersecting the ground at point B2 and its top at point F. Take point A on the mirror and draw a perpendicular from A to B2, intersecting at point B. Take points I and J, and draw a line segment from I to J, intersecting AB2 at point H. Take point M on the mirror and draw a perpendicular from M to MH, intersecting at point N. Draw a line segment from H to N, intersecting AB2 at points A' and B', and draw angle B'GA'. Draw a line segment from A' to B'. Take point P and draw a perpendicular from P to MP, intersecting at point Q, and draw a line segment from G to Q, intersecting AB2 at point R. Draw a perpendicular from R, intersecting AB2 at point U, and draw a quadrilateral USVT.
The prompt above was compiled from the original drawing commands and is for reference only.