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Constructing a 3/4 Angle Example

Constructing a 3/4 Angle Example
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2015-02-18 02:16
AngleGeometric ConstructionSlider Animation
In collections PARCC Math III Unit 5 Lesson 1
This example demonstrates how to construct an angle with a measure three-fourths that of angle ∠S using GeoGebra. It involves core mathematical concepts such as angle measurement, geometric construction, and proportional relationships. Key GeoGebra commands and objects used include Polygon, Segment, Ray, Circle, Intersect, Midpoint, Vector, Translate, CircumcircleArc, and Mirror. Suitable for high school students learning about angle proportions and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon((22, y(Corner[1])), Corner[2], Corner[3], (22, y(Corner[4]))) → mask, a, b, c, d
  2. Segment(S, U) → FirstArcDistance
  3. Ray(S, U) → FirstAngleRay1
  4. Ray(S, FirstAngleRaypt) → FirstAngleRay2
  5. Circle(S, Segment[S, U]) → CircRad1
  6. Circle(S, (2 * Segment[S, U])) → CircRad2
  7. Intersect(CircRad2, FirstAngleRay1) → Udouble,
  8. Intersect(CircRad2, FirstAngleRay2) → Tdouble,
  9. Intersect(CircRad1, FirstAngleRay2) → T,
  10. Circle(U, Udouble) → CircCenU
  11. Circle(T, Tdouble) → CircCenT
  12. Midpoint(U, T) → F
  13. Ray(S, F) → MidRay
  14. Vector(S, S + (2 * (F - S))) → ShiftVec
  15. Translate(F, ShiftVec) → Ftranslated
  16. Intersect(CircCenT, Segment[F, Ftranslated]) → W,
  17. CircumcircleArc(Tdouble, W, S) → ArcT
  18. CircumcircleArc(Udouble, W, S) → ArcU
  19. Intersect(CircRad2, MidRay) → A,
  20. Intersect(CircRad1, MidRay) → X,
  21. Midpoint(X, U) → G
  22. Ray(S, G) → ThreeQuarterRay
  23. Translate(G, Vector[(2 * Vector[S, G])]) → Gtranslated
  24. Intersect(ArcU, Segment[G, Gtranslated]) → Z,
  25. CircumcircleArc(A, Z, S) → ArcX
  26. Mirror(X, FirstAngleRay1) → FirstArcA
  27. Mirror(X, FirstAngleRay2) → FirstArcB
  28. CircumcircleArc(FirstArcB, X, FirstArcA) → FirstArc
  29. Intersect(ArcX, Segment[U, Udouble]) → B,
  30. CircumcircleArc(A, Z, B) → ArcXShort
  31. Midpoint(T, X) → C
  32. Ray(S, C) → QuarterRay
  33. Intersect(ArcT, Segment[G, Gtranslated]) → I,
  34. CircumcircleArc(Tdouble, W, I) → ArcTShort
  35. Translate(C, Vector[(2 * Vector[S, C])]) → Ctranslated
  36. Intersect(ArcU, Segment[C, Ctranslated]) → E,
  37. CircumcircleArc(Udouble, W, E) → ArcUShort
  38. Ray(S, G) → EndRay1
  39. Ray(S, FirstAngleRaypt) → EndRay2

AI Drawing Prompt Reference

Construct an angle that is three-quarters the size of the given angle ∠S. Start by drawing the two sides of ∠S, then construct a circle with center at S and twice the length of the sides. Find the intersection points of this circle with the sides of ∠S. Use these points to create new arcs and rays, gradually adjusting the angle until it is three-quarters of ∠S. Finally, use mirroring and translation to precisely determine the sides of the target angle.
The prompt above was compiled from the original drawing commands and is for reference only.