B. False
In geometry, specifically the study of triangles, there is a rule known as the Side-Side-Side (SSS) postulate. The SSS postulate states that if three sides of one triangle are congruent (that is, they have the same lengths) to three sides of another triangle, then the two triangles are congruent. Congruency in this context means that the triangles are identical in shape and size, and can be superimposed over each other through a series of rigid transformations such as translations, rotations, and reflections.
Therefore, if you have two sets of three lengths that can form triangles, and all three lengths of one set are exactly equal to the three lengths of the other, the resulting triangles will be congruent to each other. No two distinct triangles can have the same three side lengths and not be congruent. This is an established fact in Euclidean geometry and does not depend on inconsistencies in building the triangles, assuming they are constructed accurately according to the lengths given.
So, the statement "You can build two triangles that have the same side lengths but are not congruent" is false.
