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

AB

 ≅  

PQ

Constructing congruent line segments

Related topics

• Congruence defined
• Congruent lines
• Congruent angles

Congruent Triangles

• Congruent triangles
• Tests for congruence
  • 3 sides (SSS)
  • Side-Angle-Side (SAS)
  • Angle-Side-Angle (ASA)
  • Angle-Angle-Side (AAS)
  • Hypotenuse-leg (HL)
• Why AAA (angle-angle-angle) doesn't work
• Why SSA (side-side-angle) doesn't work

Congruent Polygons

• Congruent polygons
• Tests for polygon congruence