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Soccer 1v1: Positioning, Angles, and Dilations

Soccer 1v1: Positioning, Angles, and Dilations
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2020-07-07 13:04
TriangleAngleTransformationGeometric ConstructionSlider Animation
In collections Soccer & Geometry: Positions, Angles, & Dilations
This GeoGebra example uses a soccer 1v1 attacking scenario to illustrate the geometric relationships among player positioning, shooting angles, and dilations (similarity transformations). Core math concepts include angles, similar triangles, dilation, geometric transformations, and special points such as midpoints and intersections. The construction employs commands like Point, Midpoint, Line, Segment, Circle, Angle, Ray, Intersect, and Distance to create objects including the shooter, goalkeeper, goal, and shadow, with a ratio parameter controlling the dilation scale to dynamically explore how positioning affects the shooting angle. Suitable for middle or high school geometry lessons on similarity, transformations, and angle measurement, as well as interdisciplinary sports math projects that connect geometry to real-world tactical decisions.

GeoGebra Commands & Parameters

  1. Point(Circle[Shooter_1, 2]) → K_1
  2. Midpoint(Shooter_1, K_1) → Shooter
  3. Point(yAxis) → A
  4. Line(A, B) → f
  5. Point(f) → Width_1
  6. Point(f) → Goal
  7. Midpoint(Goal, Width_1) → goal
  8. Segment(goal, Shooter) → m
  9. Point(f) → C
  10. Point(f) → D
  11. Circle(goal, Shooter_1) → c
  12. Segment(Shooter_1, K_1) → h
  13. Segment(Width_1, Shooter) → g
  14. Segment(Goal, Shooter) → i
  15. Angle(Width_1, Shooter, Goal) → α
  16. Point(Circle[Goalkeeper, 2]) → Width
  17. Segment(Goalkeeper, Width) → j
  18. Ray(Shooter, Goalkeeper) → k
  19. Ray(Shooter, Width) → l
  20. Intersect(f, k) → Shadow
  21. Intersect(f, l) → Width_2
  22. Segment(Goal, Width_1) → n
  23. Midpoint(Goalkeeper, Width) → K
  24. Distance(Shooter, goal) → distanceLGoal
  25. Distance(Shooter, K) → distanceLG
  26. Distance(Shooter, K) → LG
  27. Distance(Shooter, K) → LK
  28. Distance(Goalkeeper, Width) → distanceGoalkeeperN
  29. Distance(Goal, Width_1) → distanceEF
  30. Segment(Shooter, K) → p
  31. Point(p) → GoalKeeper_1
  32. Distance(goal, Shooter) → distancegoalShooter
  33. Distance(Shooter, GoalKeeper_1) → distanceShooterGoalKeeper1
  34. Distance(Shooter, goal) → distanceShootergoal
  35. Distance(Shadow, Width_2) → distanceShadowWidth2
  36. Distance(GoalKeeper_1, goal) → distanceGoalKeeper1goal
  37. Segment(Width, Goalkeeper) → t
  38. Segment(Shadow, Width_2) → d
  39. Point(p) → F
  40. Segment(Shooter, goal) → f_1