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Proof Without Words by Steve Phelps (15)

Proof Without Words by Steve Phelps (15)
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2015-02-02 22:56
TriangleTransformationGeometric Construction
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Proofs Without Words Proofs Without Words
Drag the objects in the sketch to observe and think about what it proves. This proof without words demonstrates the midline theorem in a triangle, showing that the midline is half the length of the base through the construction of a triangle and its midline. The commands used include Point, Polygon, Midpoint, and Rotate. Suitable for junior high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Point(d) → E
  5. Midpoint(D, B) → F
  6. Rotate(E, 90*°, F) → E'
  7. Rotate(E', 90*°, F) → E''
  8. Rotate(E'', 90*°, F) → E'''
  9. Polygon(E, D, E''') → poly2, e''', e, d_1
  10. Polygon(E''', C, E'') → poly3, e'', e'''_1, c_1
  11. Polygon(E, E', A) → poly4, a_1, e_1, e'
  12. Polygon(E', E'', B) → poly5, b_1, e'_1, e''_1
  13. Midpoint(E, E''') → G
  14. Midpoint(E''', E'') → H
  15. Midpoint(E'', E') → I
  16. Midpoint(E', E) → J
  17. Rotate(E, α, G) → E'_1
  18. Rotate(D, α, G) → D'
  19. Rotate(E''', α, G) → K
  20. Polygon(E'_1, D', K) → poly2', k, e'_2, d'
  21. Rotate(E, α, J) → E'_2
  22. Rotate(E', α, J) → E''_1
  23. Rotate(A, α, J) → A'
  24. Polygon(E'_2, E''_1, A') → poly4', a', e'_3, e''_2
  25. Rotate(E', α, I) → E''_2
  26. Rotate(E'', α, I) → E'''_1
  27. Rotate(B, α, I) → B'
  28. Polygon(E''_2, E'''_1, B') → poly5', b', e''_3, e'''_2
  29. Rotate(E''', α, H) → M
  30. Rotate(C, α, H) → C'
  31. Rotate(E'', α, H) → E'''_2
  32. Polygon(M, C', E'''_2) → poly3', e'''_3, m, c'

AI Drawing Prompt Reference

Draw a triangle ABC, then take the midpoint D on side BC. Rotate point E 90 degrees clockwise around D to get E', then rotate E' 90 degrees clockwise around D to get E'', and finally rotate E'' 90 degrees clockwise around D to get E'''. Connect DE'''. Through rotation and construction, observe and understand the midline theorem, which states that the midline is half the length of the base.
The prompt above was compiled from the original drawing commands and is for reference only.