Rapidly-exploring Random Tree (RRT)-based algorithms have become increasingly popular due to their lower computational complexity as compared with other path planning algorithms. The recently presented RRT * motion planning algorithm improves upon the original RRT algorithm by providing optimal path solutions. While RRT determines an initial collision-free path fairly quickly, RRT * guarantees almost certain convergence to an optimal, obstacle-free path from the start to the goal points for any given geometrical environment. However, the main limitations of RRT * include its slow processing rate and high memory consumption, due to the large number of iterations required for calculating the optimal path. In order to overcome these limitations, we present another improvement, i.e, the Triangular Geometerized-RRT * (TG-RRT * ) algorithm, which utilizes triangular geometrical methods to improve the performance of the RRT * algorithm in terms of the processing time and a decreased number of iterations required for an optimal path solution. Simulations comparing the performance results of the improved TG-RRT * with RRT * are presented to demonstrate the overall improvement in performance and optimal path detection.