The line of symmetry of a line segment is the _____ bisector of the line segment.
perpendicular bisector.
35. The line of symmetry of a line segment is the _____ bisector of the line segment.
Answer: perpendicular bisector.
Take a line segment with two endpoints. Let’s name them (A) and (B).
( ext{Segment } overline{AB})
Find the middle point of the segment. This point is called the midpoint, say (M).
(M ext{ is halfway between } A ext{ and } B)
(AM = MB)
Draw a new line that passes through the midpoint (M).
(ell ext{ passes through } M)
Make sure this new line is at a right angle (90°) to the segment (overline{AB}).
(ell perp overline{AB})
(angle(ell, overline{AB}) = 90^circ)
This special line does two things:
Now, if you fold the segment along this line, point (A) lands exactly on point (B), and the two halves match perfectly.
( ext{Reflection across } ell: A leftrightarrow B)
Because folding (or reflecting) across this line makes the two sides match, this line is a line of symmetry for the segment.
Key idea: The line of symmetry for a line segment is the line that goes through its midpoint and is at right angles to it — the perpendicular bisector.
(oxed{ ext{Line of symmetry of } overline{AB} = ext{ Perpendicular Bisector at } M})