Geodesic triangles are formed by three points on a Riemannian manifold, with each side of the triangle being a geodesic segment connecting these points. These triangles play a significant role in understanding the geometric properties of curved spaces and help in visualizing the relationships between distances and angles in Riemannian geometry. The study of geodesic triangles is crucial for results like Toponogov's theorem, which relates the geometry of triangles in spaces of constant curvature.
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