Feature correspondence is one of the essential difficulties in image processing, given that it is applied within a wide range in computer vision. Even though it has been studied for many years, feature correspondence is still far from being ideal. This paper proposes a multigeometric-constraint algorithm for finding correspondences between two sets of features. It does so by considering interior angles and edge lengths of triangles formed by third-order tuples of points. Multigeometric-constraints are formulated using matrices representing triangle similarities. The experimental evaluation showed that the multigeometric-constraint algorithm can significantly improve the matching precision and is robust to most geometric and photometric transformations including rotation, scale change, blur, viewpoint change, and JPEG compression as well as illumination change. The multigeometric-constraint algorithm was applied to object recognition which includes extraprocessing and affine transformation. The results showed that this approach works well for this recognition.