Question & Answer

When are two line segments congruent?

ANSWER Verified Verified
Hint: Line segment is a part of the line which has both starting point and endpoint. Line segments having the same length can be considered for congruency.

Complete step-by-step answer:
A line is a straight one-dimensional figure with no thickness. It extends endlessly in both directions.
A line segment is a part of a line that has a starting point and an endpoint. A line segment has a finite length.
Two or more line segments are said to be congruent if they have the same length. They don't need to be parallel. They can be oriented in any direction. Length is the only condition for them to be congruent.
The congruency can be found by dragging the starting point of one line segment to intersect with the other. Then, this line segment is rotated with the starting point as the center such that both become coincident. Now, if they are equal in length, then they are congruent, if they are not equal in length, then they are not congruent.
If line segment AB is congruent to CD, then they are represented as below:
\[\overline {AB} \cong \overline {CD} \]
In contrast, congruence is not defined for rays and lines because both of them do not have finite length.
Hence, the two lines are congruent if they are equal in length.

Note: You might think that the line segments are congruent only if they are in the same direction. But for a line segment, it is free to be rotated in space, hence, the length is the deciding factor.