Final answer:
Two equilateral triangles with sides of different lengths are similar because they have the same shape, but they are not congruent since they do not have the same size.
Step-by-step explanation:
To determine whether two triangles are congruent, similar, or both, we must compare their sides and angles.
A triangle with all sides equal is called an equilateral triangle, and all its internal angles are also equal, with each measuring 60 degrees.
If we have two triangles, one with sides of length 10 and the other with sides of length 6, and both are equilateral, these triangles are similar because they have the same shape but different sizes.
However, they are not congruent because their sides are not of equal length. Two figures are congruent if they are the same size and shape, which is not the case here.