Final answer:
Konnor's conclusion is incorrect if based solely on congruent angles; to conclude similarity, corresponding sides must also be in proportion. If only angles are considered, quadrilaterals could be congruent or not similar at all.
Step-by-step explanation:
Konnor's statement that 'The quadrilaterals have four pairs of congruent corresponding angles, so the figures are similar' falls under the category of geometric similarity. In geometry, two figures are similar if they have the same shape, which means corresponding angles are congruent and corresponding sides are in proportion. However, simply having congruent corresponding angles does not ensure similarity; the sides must also be proportional. If only the angles are congruent and not the sides, the quadrilaterals could still vary in size. Therefore, Konnor's conclusion is erroneous if he is asserting similarity solely based on angle congruency without verifying side proportionality. In that case, it is possible that the correct conclusion should be that the quadrilaterals are congruent, not similar (Option A), or that it's impossible to map the figures onto each other using only rigid transformations and dilations, meaning they are not similar (Option B). For the quadrilaterals to be similar, Konnor would need to demonstrate that in addition to having congruent angles, the sides of the quadrilaterals are proportional in length. Congruent angles is a necessary condition for similarity, but it is not a sufficient condition without also having side proportionality.