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Construct an Angle Double the Given Angle

Construct an Angle Double the Given Angle
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2015-02-18 01:54
AngleTransformationGeometric Construction
In collections PARCC Math III Unit 5 Lesson 1
This example demonstrates how to construct a new angle equal to twice a given angle using GeoGebra. It involves core mathematical concepts such as angles, straight lines, angle addition, and intersection. The construction utilizes commands like Polygon, Segment, Ray, Vector, Translate, Circle, Intersect, Mirror, and CircumcircleArc to achieve the desired angle construction and transformation. Suitable for high school students learning geometric constructions and angle operations.

GeoGebra Commands & Parameters

  1. Polygon((22, y(Corner[1])), Corner[2], Corner[3], (22, y(Corner[4]))) → mask, a, b, c, d
  2. Segment(A, B) → FirstArcDistance
  3. Ray(G, RayPoint) → SecondAngleRayMid
  4. Vector(A, G) → u
  5. Translate(A, u) → A'
  6. Translate(B, u) → TranslateB
  7. Segment(A', TranslateB) → FirstTranslation
  8. Circle(G, TranslateB) → SecondAngleCircle
  9. Intersect(SecondAngleCircle, SecondAngleRayMid) → H,
  10. Vector(G, H) → v
  11. Ray(A, B) → FirstAngleRay1
  12. Ray(A, FirstAngleRaypt) → FirstAngleRay2
  13. Circle(A, B) → FirstAngleCircle
  14. Intersect(FirstAngleCircle, FirstAngleRay2) → C,
  15. Mirror(B, FirstAngleRay2) → FirstAngleDef1
  16. Mirror(C, FirstAngleRay1) → FirstAngleDef2
  17. Segment(C, B) → AcrossFistArc
  18. CircumcircleArc(FirstAngleDef1, B, FirstAngleDef2) → FirstAngleArc
  19. Segment(B, FirstAngleDef1) → BuildLength
  20. Circle(H, AcrossFistArc) → BetweenSecondAngle
  21. Intersect(BetweenSecondAngle, SecondAngleCircle) → J, E, ,
  22. Ray(G, J) → SecondAngleRay2
  23. Mirror(H, SecondAngleRay2) → SecondAngleDef2
  24. Ray(G, E) → SecondAngleRay1
  25. Mirror(H, SecondAngleRay1) → SecondAngleDef1
  26. CircumcircleArc(SecondAngleDef1, H, SecondAngleDef2) → SecondAngleArc
  27. Segment(E, H) → AcrossSecondArc

AI Drawing Prompt Reference

Construct an angle that is double the given angle. Start by drawing a quadrilateral and identifying its vertices. Then, use a point and vector to construct two rays and a segment. Utilize circles and intersections to find key points, and construct the new angle through mirroring and arcs. Finally, connect the key points to form the desired double angle.
The prompt above was compiled from the original drawing commands and is for reference only.