Proof that Congruent Opposite Angles Imply Parallelogram

Proof that Congruent Opposite Angles Imply Parallelogram
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2017-10-12 11:01
This example demonstrates how to dynamically prove the theorem that congruent opposite angles imply a parallelogram using GeoGebra. It involves core mathematical concepts such as angles, parallel lines, opposite angles, and the criteria for determining parallelograms. The construction uses commands like Line, Intersect, Angle, and Segment to build the geometric figure and measure angles. Suitable for middle school students and above to learn and understand the criteria for parallelograms, as well as for geometry proof teaching purposes.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(C, f) → g
  3. Line(A, C) → h
  4. Line(B, h) → i
  5. Intersect(g, i) → D
  6. Angle(A, C, D) → α
  7. Angle(A, B, D) → β
  8. Angle(C, A, B) → γ
  9. Angle(B, D, C) → δ
  10. Segment(C, B) → j
  11. Angle(B, C, D) → ε
  12. Angle(A, B, C) → ζ