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Angles of an Isosceles Trapezoid (Bilingual)

Angles of an Isosceles Trapezoid (Bilingual)
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2017-10-13 17:45
PolygonAngleTransformationGeometric ConstructionSlider Animation
In collections Quadrilaterals الرُباعيات
① This interactive GeoGebra example visually demonstrates the angle relationships in an isosceles trapezoid, with labels in English and Arabic. ② The core mathematical concept is the property of isosceles trapezoids: base angles on the same base are equal, and consecutive angles are supplementary (sum to 180°). ③ Construction details: the trapezoid is built using Segment, Translate, Vector, and Rotate commands; four angles (α, β, γ, δ) are marked with the Angle tool; buttons (button1–button4) toggle language displays, and text objects (text1–text6) provide labels. ④ Suitable for middle school geometry lessons or self-study, especially in bilingual classrooms, to explore and verify the angle properties of isosceles trapezoids interactively.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(D, A) → i
  4. Segment(D, C) → h
  5. Angle(D, A, B) → α
  6. Angle(A, B, C) → β
  7. Angle(B, C, D) → γ
  8. Angle(C, D, A) → δ
  9. Translate(C, Vector[(a * Vector[C, D])]) → C1
  10. Translate(B, Vector[(a * Vector[C, D])]) → B1
  11. Vector(C, D) → u
  12. Vector(B, A) → v
  13. Segment(B1, C1) → j
  14. Rotate(B1, (-((b * (180° - (2 * γ))))), C1) → B2
  15. Segment(C1, B2) → k

AI Drawing Prompt Reference

Draw an isosceles trapezoid, highlighting that its base angles are equal and consecutive angles sum to 180°. Label the four angles α, β, γ, δ with different colors and add text explaining their relationships. Include a movable vector to construct the other side of the trapezoid via translation and rotation, with a slider to control the transformation.
The prompt above was compiled from the original drawing commands and is for reference only.