Vertical Angle Theorem
When two straight lines intersect at a point, four angles are made. The non-adjacent angles are called vertical or opposite or vertically opposite angles. Also, each pair of adjacent angles forms a straight line and the two angles are supplementary. Since either of a pair of vertical angles is supplementary to either of the adjacent angles, the vertical angles are equal in measure. Eudemus of Rhodes attributed the proof of this theorem to Thales of Miletus. According to a historical Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.
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