Contact-based biometric applications primarily use prints from a finger or a palm for a single instance in different applications. For access control, there is an enrollment process using one or more templates which are compared with verification images. In forensics applications, randomly located, partial, and often degraded prints acquired from a crime scene are compared with the images captured from suspects or existing fingerprint databases, like AFIS. In both scenarios, if we need to use handprints which include segments from the finger and palm, what would be the solution? The motivation behind this is the concept of one single algorithm for one hand. Using an algorithm that can incorporate both prints in a common processing framework can be an alternative which will have advantages like scaling to larger existing databases. This work proposes a method that uses minutiae or minutiae-like features, Delaunay triangulation and graph matching with invariant feature representation to overcome the effects of rotation and scaling. Since palm prints have a large surface area with degradation, they tend to have many false minutiae compared to fingerprints, and the existing palm print algorithms fail to tackle this. The proposed algorithm constructs Delaunay triangulated graphs (DTG) using minutiae where Delaunay triangles form from minutiae, and initiate a collection of base triangles for opening the matching process. Several matches may be observed for a single triangle match when two images are compared. Therefore, the set of initially matched triangles may not be a true set of matched triangles. Each matched triangle is then used to extend as a sub-graph, adding more nodes to it until a maximum graph size is reached. When a significant region of the template image is matched with the test image, the highest possible order of this graph will be obtained. To prove the robustness of the algorithm to geometrical variations and working ability with extremely degraded (similar to latent prints) conditions, it is demonstrated with a subset of partial-quality and extremely-low-quality images from the FVC (fingerprint) and the THUPALMLAB (palm print) databases with and without geometrical variations. The algorithm is useful when partial matches between template and test are expected, and alignment or geometrical normalization is not accurately possible in pre-processing. It will also work for cross-comparisons between images that are not known a priori.