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Exploring Polygon Congruence

Exploring Polygon Congruence
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2018-01-20 00:39
PolygonGeometric Construction
This example demonstrates how to determine if polygons are congruent through transformations. Key concepts include congruence, translation, rotation, and random number generation. It uses commands like Polygon, Translate, and Random to create and manipulate polygons. Suitable for middle school and above, helping students understand geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. Polygon((1.5, 2), (3.5, 2), (4, 3), (3, 5), (1, 4)) → Pent1, m, n, p, q, r
  2. Polygon((1, 2), (4, 2), (2, 5)) → Triangle1, f, g, h
  3. Polygon((1, 2), (4, 2), (4, 5), (2, 4)) → Quad1, i, j, k, l
  4. Polygon((7.3, 5.8), (9.8, 5.8), (9.8, 6.5), (7.3, 6.5)) → Box1, s, t, b, c
  5. Translate(Rotate[Translate[Rotate[Pent1, RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2
  6. Polygon((10, 5.8), (12.5, 5.8), (12.5, 6.5), (10, 6.5)) → Box2, d, e, f_1, g_1
  7. Translate(Rotate[Translate[Rotate[Triangle1, RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2
  8. Translate(Rotate[Translate[Rotate[Quad1, RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2
  9. Random(1, 3) → ans
  10. Translate(Rotate[Translate[Rotate[Polygon[(2, 2), (4, 2), (2, 5)], RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2Wrong1
  11. Translate(Rotate[Translate[Rotate[Dilate[Triangle1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], a, RotPt2], (move, 0)) → Triangle2Wrong2
  12. Translate(Rotate[Translate[Rotate[Polygon[(1, 2), (4, 2), (4, 4), (2, 4)], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2Wrong1
  13. Translate(Rotate[Translate[Rotate[Dilate[Quad1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Quad2Wrong2
  14. Translate(Rotate[Translate[Rotate[Polygon[(1.5, 2), (3.5, 2), (4, 3), (3, 5), (1, 3)], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2Wrong1
  15. Translate(Rotate[Translate[Rotate[Dilate[Pent1, 0.7, RotPt], RotAngle, RotPt], (8, 0)], (a * 10), RotPt2], (move, 0)) → Pent2Wrong2
  16. Translate(RotPt2 + (-0.3, 0.4), (move, 0)) → LabBPt