Final answer:
Triangles EGL and LGE are congruent, as congruency in geometry means triangles have corresponding angles and sides that match, and the names EGL and LGE represent the same vertices in a different order.
Step-by-step explanation:
The question involves determining which triangle is congruent to another. In the context of geometry, congruent triangles are triangles that have exactly the same size and shape, meaning all corresponding sides and angles match. When we look at the names of the triangles provided in the options—EFG, GLE, LGE, and EGL—we notice that they have the same letters but in different orders. Congruent triangles can be rotated or flipped, but the congruency refers to the matching of angles and sides in sequence. For example, triangle EGL will have the same angles and sides, in the same order, as triangle LGE, but triangle EGL is not congruent to itself since congruency implies two distinct triangles.