Opposite angles are equal

Take two intersecting lines:

  \
 A \ B
-------
 C  \D
     \
A + B = 180 (def of line)
C + D = 180 (def of line)
B + D = 180 (def of line)
C + A = 180 (def of line)
Therefore
A + B = B + D (equality)
A = D (subtract B from each side)
Therefore oppsite angle are equal

Is that not a work of art? Its simplicity and elegance, one of the basic corner stones of Euclidean geometry. (I make no claims as to its originality)

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