<p>Graphic statics, an old-timer classic method in structural analysis, stands out for its effectiveness and visual appeal in analyzing statically determinate planar trusses using two reciprocal diagrams. However, since it only uses geometric construction to represent the equilibrium of force vectors, it does not involve structural deformation, and thus cannot solve the redundant reactions in statically indeterminate trusses. By incorporating the recently established matrix-algebraic operation on reciprocal diagrams and the unit load method for finding joint displacements, this study is dedicated to developing a methodology for solving externally indeterminate trusses. A key innovation is the introduction of a novel vertex-extrapolated form diagram, constructed by adding virtual vertices and edges at the original truss joints. The incidence matrix of the vertex-extrapolated form diagram can effectively simplify the application of unit loads when using the principle of virtual work. To solve indeterminate trusses, redundant supports are removed by setting their force densities to zero, and compatibility conditions are satisfied by solving the displacement equations. Overall, the approach is well suited to computer-aided design (CAD) environment, leveraging matrix operations for automated analysis. The validity and accuracy of the proposed methodology are demonstrated through practical examples involving both determinate and indeterminate trusses.</p>