Summary: A signed graph (marked graph) is an ordered pair \(S=(G,\sigma)\) (\(s=(G,\mu)\)), where \(G=(V,E)\) is a graph called the underlying graph of \(S\) and \(\sigma:E\to \{+,-\}\) \((\mu:V\to\{+,-\})\) is a function. The triangular line graph of a graph \(G=(V,E)\) is a graph \({\mathcal T}(G)=(V',E')\) with vertex set \(V'=E(G)\) such that two vertices \(e\) and \(f\) are adjacent if and only if the corresponding edges in \(G\) belong to a triangle of \(G\). Analogously, we define the triangular line signed graph of a signed graph \(S=(G,\sigma)\) as a signed graph \({\mathcal T}(S)= ({\mathcal T}(G),\sigma')\) where \({\mathcal T}(G)\) is the underlying graph of \({\mathcal T}(S)\), where for any edge \((e_1,e_2)\) in \({\mathcal T}(S)\), \(\sigma'(e_1,e_2)= \sigma(e_1)\sigma(e_2)\). It is shown that for any signed graph \(S\), its triangular line signed graph \({\mathcal T}(S)\) is balanced. Two signed graphs \(S_1\) and \(S_2\) are switching equivalent written \(S_1\sim S_2\), whenever there exists a marking \(\mu\) of \(S_1\) such that the signed graph \(S_\mu(S_1)\) obtained by changing the sign of every edge of \(S_1\) to its opposite whenever its end vertices are of opposite signs, is isomorphic to \(S_2\). Further, a structural characterization of signed graphs that are switching equivalent to their line signed graphs is obtained.