Final answer:
Bisecting an angle is the only construction among the options provided that does not begin with a line segment.
Step-by-step explanation:
Out of the constructions given, the one that doesn't start with a line segment is 1) Bisecting an angle. Bisecting an angle involves drawing a line that splits an existing angle into two equal parts, and does not necessarily require a line segment as a starting point.
On the other hand, constructing a parallel line, constructing a perpendicular line, and constructing a triangle with given sides, all call for a line segment to begin the construction process.This process continues for long.
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