Axial Symmetry Demo

Axial Symmetry Demo
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2014-10-05 01:06
This example demonstrates the construction and properties of axially symmetric figures. By drawing the symmetric point B of point A across the median line, it visually illustrates the symmetry relationship. Core mathematical concepts include axial symmetry, median line, geometric construction, and geometric transformations. The construction utilizes GeoGebra commands and objects such as Line, OrthogonalLine, Mirror, Segment, and Point. It is suitable for middle school and above students learning geometric transformations, symmetry, and construction techniques, as well as for visualizing symmetric distributions in probability & statistics.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(C, a) → b
  3. Mirror(pic1, a) → pic1'
  4. Mirror(pic1, b) → pic1'_1
  5. Segment(D, E) → c
  6. Segment(F, G) → d
  7. Segment(F, H) → e
  8. Segment(D, I) → f
  9. Line(J, K) → i
  10. Mirror(pic1, i) → pic1'_2
  11. Mirror(F, i) → F'
  12. Mirror(D, i) → D'
  13. Segment(F, F') → k
  14. Segment(D, D') → l
  15. Point(b) → L

AI Drawing Prompt Reference

Draw an axially symmetric figure by first drawing a line AB, then drawing a line CD perpendicular to AB. Next, reflect point A across line AB to get point A', and reflect point A' across line CD to get point A''. Connect points D and E, F and G, F and H, and D and I. Draw a line JK, reflect point D across line JK to get point D', and reflect point F across line JK to get point F'. Connect points F and F', D and D', and finally take a point L on line CD.
The prompt above was compiled from the original drawing commands and is for reference only.