MathPlotAI Logo MathPlotAI

Congruent Supplements of the Same Angle Proof

Congruent Supplements of the Same Angle Proof
Loading the math board and drawing, please wait…
2016-10-20 03:20
AngleTrigonometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates the geometric proof of congruent supplements of the same angle. Core math concepts include angles, supplementary angles, and geometric construction. It utilizes GeoGebra commands/objects such as Ray, Rotate, Angle, Circle, Line, Intersect, LaTeX, CircleSector, Dilate, Vector, Translate, Point, and CircleArc. Suitable for high school geometry proof teaching or learning.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Circle(A, 1) → c
  6. Line(B, A) → h
  7. Intersect(c, h, 2) → C
  8. Ray(A, C) → i
  9. Ray(D, E) → j
  10. Rotate(E, α, D) → E'
  11. Angle(E, D, E') → γ
  12. Ray(D, E') → k
  13. Line(E, D) → l
  14. Circle(D, 1) → d
  15. Intersect(d, l, 2) → F
  16. Ray(D, F) → m
  17. LaTeX(B', true, true) → text1
  18. Circle(D, 2) → e
  19. Intersect(e, j, 1) → G
  20. Intersect(e, k, 1) → H
  21. Line(D, i) → n
  22. CircleSector(D, G, H) → p
  23. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], A) → D'
  24. Vector(D, D') → u
  25. Translate(p, u) → p'
  26. Point(n) → I
  27. Angle(I, D, E') → δ
  28. Line(D, g) → q
  29. Intersect(e, q, 2) → J
  30. Angle(H, D, J) → ε
  31. Rotate(p', If[0 < a ≤ 1, (a * ε), ε], D') → p''
  32. CircleArc(D, G, H) → r
  33. Intersect(e, m) → K,
  34. CircleSector(D, H, K) → s
  35. Dilate(D, If[2.75 < a ≤ 3.75, 3.75 - a, 0], A) → D'_1
  36. Vector(D, D'_1) → v
  37. Translate(s, v) → s'
  38. Rotate(s', If[2.75 < a ≤ 3.75, ((a - 2.75) * ε), ε], D'_1) → s''
  39. CircleArc(D, H, K) → t

AI Drawing Prompt Reference

Draw a proof of congruent supplements of the same angle. Start by drawing angle A and B, then rotate B to get B' and angle β. Draw a circle and a line, find intersection points C and D, construct angle E' and angle γ. Use rotation and circle intersections to find angles δ and ε. Finally, use rotation and scaling to construct arcs and sectors, completing the proof of congruent supplements of the same angle.
The prompt above was compiled from the original drawing commands and is for reference only.