diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,9 @@
+## [v1.5.1](https://github.com/diagrams/diagrams-lib/tree/v1.5.1) (2025-12-02)
+
+- New `Semigroup` instance for located lines (i.e. `Located (Trail'
+  Line v n)`), which adds an extra segment from the end of the first
+  to the start of the second.
+
 ## [v1.5.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.5.0.1) (2025-08-25)
 
 - Fix bug in `bezierFindRoot` that caused diagrams to hang when
diff --git a/diagrams-lib.cabal b/diagrams-lib.cabal
--- a/diagrams-lib.cabal
+++ b/diagrams-lib.cabal
@@ -1,5 +1,5 @@
 Name:                diagrams-lib
-Version:             1.5.0.1
+Version:             1.5.1
 Synopsis:            Embedded domain-specific language for declarative graphics
 Description:         Diagrams is a flexible, extensible EDSL for creating
                      graphics of many types.  Graphics can be created
diff --git a/src/Diagrams/Trail.hs b/src/Diagrams/Trail.hs
--- a/src/Diagrams/Trail.hs
+++ b/src/Diagrams/Trail.hs
@@ -539,6 +539,17 @@
   _Snoc = _Wrapped . _Snoc . bimapping _Unwrapped id
   {-# INLINE _Snoc #-}
 
+-- | Compose two Located trails by adding a segment joining the endpoint
+--   of the first to the starting point of the second.  Note, if you have
+--   two located trails such that the end of the first coincides with the
+--   start of the second, this will still add a trivial zero-length segment
+--   between them; in that case you are probably better off with something
+--   like @mapLoc (<> unLoc t2) t1@.
+instance (Real n, Floating n, Metric v)
+  => Semigroup (Located (Trail' Line v n)) where
+    a@(Loc aLoc aLine) <> b@(Loc _ bLine) =
+      Loc aLoc (aLine <> lineFromOffsets [atStart b .-. atEnd a] <> bLine)
+
 --------------------------------------------------
 -- Extracting segments