Brain tumors, particularly malignant ones, can be fatal if not properly diagnosed. Early diagnosis of brain tumors is crucial for improving patient outcomes and increasing the chances of full recovery. In addition to laboratory analyses, clinicians and surgeons rely on information extracted from medical images, such as those obtained through magnetic resonance imaging (MRI), to accurately detect and characterize brain tumors. This paper proposes novel methods for classifying and segmenting brain MRI images using information geometric techniques. We present (1) a feature-based method using gray level co-occurrence matrix (GLCM) and embedding space of univariate Gaussian distribution into symmetric positive definite (SPD) matrices for classification, and (2) a pixel-wise approach constructing a statistical manifold of univariate normal distributions, where each pixel is represented as a point on this manifold and segmentation is done using the Fisher distance. The GLCM features are classified using K-nearest neighbor with various distance measures on the SPD manifold, while the segmentation utilizes K-means clustering with Fisher distance on the statistical manifold. Evaluating our methods on 178 brain MRI images, we achieve promising results in tumor classification and region segmentation, with the Log-Frobenius distance metric showing the highest classification accuracy of 82.86%.