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Opposite Angles of a Parallelogram (Bilingual Arabic/English)

Opposite Angles of a Parallelogram (Bilingual Arabic/English)
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2017-10-13 17:03
PolygonAngleTransformationGeometric ConstructionSlider Animation
In collections Quadrilaterals الرُباعيات
① This interactive GeoGebra example demonstrates that opposite angles of a parallelogram are equal, with bilingual labels in Arabic and English. ② The core mathematical concept is the parallelogram angle theorem, involving polygon interior angles, rotational symmetry, and angle measurement. ③ Construction details: The quadrilateral poly1 is built using the Polygon command; angles α, β, γ, δ are marked with the Angle command; Intersect finds intersection points; Rotate is used to rotate the figure for visual comparison; buttons (button1, button2, etc.) toggle language or show answers, while text objects (text1–text6) provide bilingual explanations. ④ Suitable for middle school geometry lessons or bilingual math classrooms, this dynamic worksheet helps students explore parallelogram properties and understand why opposite angles are equal through rotation and measurement.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Angle(C, D, A) → α
  3. Intersect(Segment[A, C], Segment[B, D]) → O
  4. Rotate(C, ((e * 180))°, O) → C1
  5. Rotate(D, ((e * 180))°, O) → D1
  6. Rotate(A, ((e * 180))°, O) → A1
  7. Angle(C1, D1, A1) → β
  8. Angle(D, A, B) → γ
  9. Rotate(D, ((h * 180))°, O) → D2
  10. Rotate(A, ((h * 180))°, O) → A2
  11. Rotate(B, ((h * 180))°, O) → B2
  12. Angle(D2, A2, B2) → δ

AI Drawing Prompt Reference

Draw a parallelogram and label its four interior angles α, β, γ, δ, demonstrating that opposite angles are equal. Start by constructing the quadrilateral, then measure and mark all four angles. Find the intersection point O of the diagonals AC and BD. Rotate vertices C, D, and A around O by 180 degrees to get C1, D1, and A1, and measure the angle β. Similarly, rotate D, A, and B around O by 180 degrees to get D2, A2, and B2, and measure the angle δ. The rotations show that α=β and γ=δ, proving the property that opposite angles of a parallelogram are equal.
The prompt above was compiled from the original drawing commands and is for reference only.