Point G is a centroid in the figure of Triangle A B C, Triangle F D E, and Triangle L M N. A centroid is the point where the medians of a triangle intersect, and each median connects a vertex to the midpoint of the opposite side.
In the context of the triangles you provided:
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For Triangle A B C, if the lines drawn from each vertex to the opposite side (the medians) intersect at point G, then G is the centroid.
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In Triangle F D E, if the line segments split each side into two equal parts, that typically implies that these lines are also medians, making G the centroid.
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In Triangle L M N, unless specified that the lines are medians, it's less clear; the unique angles suggested may not relate directly to the characteristics of centroids.
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Triangle H J K mentions lines forming right angles, which does not inform us about the lines being medians with respect to a centroid.
Therefore, based on the definitions, point G is definitively identified as a centroid in Triangles A B C and F D E. Triangle F D E, where lines are drawn from each point to the opposite side and split each side into equal parts, would definitively indicate that G is the centroid. If Triangle F D E satisfies that condition of equal partitioning of the opposite sides, then point G is a centroid there as well.
So, in conclusion, without extra specification, the clear candidates for centroids based on median intersection characteristics are Triangle A B C and Triangle F D E.