diff --git a/stdlib/LinearAlgebra/src/lu.jl b/stdlib/LinearAlgebra/src/lu.jl
index d2e82af5d6409..0837ac08e74ea 100644
--- a/stdlib/LinearAlgebra/src/lu.jl
+++ b/stdlib/LinearAlgebra/src/lu.jl
@@ -786,7 +786,7 @@ function ldiv!(adjA::AdjointFactorization{<:Any,<:LU{T,Tridiagonal{T,V}}}, B::Ab
     return B
 end
 
-rdiv!(B::AbstractMatrix, A::LU) = transpose(ldiv!(transpose(A), transpose(B)))
+rdiv!(B::AbstractMatrix, A::LU{T,Tridiagonal{T,V}}) where {T,V} = transpose(ldiv!(transpose(A), transpose(B)))
 
 # Conversions
 AbstractMatrix(F::LU) = (F.L * F.U)[invperm(F.p),:]
diff --git a/stdlib/LinearAlgebra/src/triangular.jl b/stdlib/LinearAlgebra/src/triangular.jl
index 1a7d04115c97d..71b0fa53816bf 100644
--- a/stdlib/LinearAlgebra/src/triangular.jl
+++ b/stdlib/LinearAlgebra/src/triangular.jl
@@ -1048,16 +1048,16 @@ _trimul!(C::AbstractMatrix, A::AbstractTriangular, B::UpperOrLowerTriangular) =
 
 function lmul!(A::AbstractTriangular, B::AbstractVecOrMat)
     if istriu(A)
-        _trimul!(B, UpperTriangular(A), B)
+        _trimul!(B, uppertriangular(A), B)
     else
-        _trimul!(B, LowerTriangular(A), B)
+        _trimul!(B, lowertriangular(A), B)
     end
 end
 function rmul!(A::AbstractMatrix, B::AbstractTriangular)
     if istriu(B)
-        _trimul!(A, A, UpperTriangular(B))
+        _trimul!(A, A, uppertriangular(B))
     else
-        _trimul!(A, A, LowerTriangular(B))
+        _trimul!(A, A, lowertriangular(B))
     end
 end
 
@@ -1097,16 +1097,16 @@ _rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::UpperOrLowerTriangular) =
 
 function ldiv!(A::AbstractTriangular, B::AbstractVecOrMat)
     if istriu(A)
-        _ldiv!(B, UpperTriangular(A), B)
+        _ldiv!(B, uppertriangular(A), B)
     else
-        _ldiv!(B, LowerTriangular(A), B)
+        _ldiv!(B, lowertriangular(A), B)
     end
 end
 function rdiv!(A::AbstractMatrix, B::AbstractTriangular)
     if istriu(B)
-        _rdiv!(A, A, UpperTriangular(B))
+        _rdiv!(A, A, uppertriangular(B))
     else
-        _rdiv!(A, A, LowerTriangular(B))
+        _rdiv!(A, A, lowertriangular(B))
     end
 end