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SAS Triangle Congruence Practice

SAS Triangle Congruence Practice
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2020-11-16 23:06
TriangleTransformationGeometric Construction
This exercise helps students identify the SAS (Side-Angle-Side) pattern for triangle congruence. Using GeoGebra commands such as Polygon, Centroid, Rotate, Dilate, Segment, and Angle, students can visually understand the concept of triangle congruence. Suitable for middle school geometry lessons.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Centroid(t1) → D
  3. Rotate(A, (π * p), D) → A'
  4. Rotate(B, (π * p), D) → B'
  5. Rotate(C, (π * p), D) → C'
  6. Dilate(Translate[A', (d, 0)], e, D) → A''
  7. Polygon(A', B', C') → t1', c', a', b'
  8. Dilate(Translate[B', (d, 0)], e, D) → B''
  9. Dilate(Translate[C', (d, 0)], e, D) → C''
  10. Polygon(A'', B'', C'') → t1'', c'', a'', b''
  11. Segment(A, B) → l
  12. Segment(B, C) → m
  13. Segment(C, A) → n
  14. Segment(A'', B'') → p_1
  15. Segment(B'', C'') → q
  16. Segment(C'', A'') → r
  17. Angle(C, A, B) → α
  18. Angle(A, B, C) → β
  19. Angle(B, C, A) → γ
  20. Angle(C'', A'', B'') → δ
  21. Angle(A'', B'', C'') → ε
  22. Angle(B'', C'', A'') → ζ

AI Drawing Prompt Reference

Draw a triangle and rotate it 180 degrees about its centroid to form a second triangle. Then translate and dilate the second triangle to create a third triangle. Show that the three triangles are congruent by SAS (Side-Angle-Side). Label all sides and angles of each triangle, and indicate corresponding equal sides and angles. The figure should clearly illustrate the transformations of rotation, translation, and scaling for students to observe congruence properties.
The prompt above was compiled from the original drawing commands and is for reference only.