Congruent Line Segments
Definition: Line segments are congruent if they have the same length
Try this Adjust any line segment below by dragging an orange dot at its ends. The other line segment will change to remain congruent with it.

Line segments are congruent if they have the same length. However, they need not be parallel. They can be at any angle or orientation on the plane. In the figure above, there are two congruent line segments. Note they are laying at different angles. If you drag any of the four endpoints, the other segment will change length to remain congruent with the one you are changing.

For line segments, 'congruent' is similar to saying 'equals'. You could say "the length of line AB equals the length of line PQ". But in geometry, the correct way to say it is "line segments AB and PQ are congruent" or, "AB is congruent to PQ".

In the figure above, note the single 'tic' marks on the lines. These are a graphical way to show that the two line segments are congruent.

Rays and lines cannot be congruent because they do not have both end points defined, and so have no definite length.

## Symbols

The symbol for congruence is

Also, recall that the symbol for a line segment is a bar over two letters, so the statement is read as "The line segment AB is congruent to the line segment PQ".

## Constructing congruent line segments

It is possible to construct (draw) a line segment that is congruent to a given segment with a compass and straightedge. For more on this see Copying a line segment.
While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref