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if one quantity equals a second and the second equals a third, then the first equals the third
if a point is not on a line segment, then a perpendicular from the point to the line segment can be constructed
if a transversal forms equal alt. interior angles with two line segments, then the line segments form parallels
there is exactly one parallel to a given line through a point that is not on the line
if a transversal form equal corresponding angles with two line segments, then the line segments are parallel
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