Question

circles a and b coincide.
alex concluded:
\circles a and b have no sides or angles with the same measurement, so the circles are not congruent.\
what error did alex make in their conclusion?
choose 1 answer:
a the circles are mapped onto each other, so they are congruent.
b the circles are not congruent, because no transformations were used.
c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Alex's conclusion, we analyze the concept of congruent circles. Congruent circles have the same radius (or diameter). If two circles coincide (as given for Circles A and B), they can be mapped onto each other (e.g., by translation, rotation, or reflection), meaning they are congruent. Alex incorrectly thought they aren't congruent by focusing on sides/angles (circles don't have sides/angles in the way polygons do, and their congruence is based on radius). Option A correctly states that since the circles are mapped onto each other, they are congruent, identifying Alex's error. Option B is wrong because congruence of circles doesn't require transformations to be applied, just the ability to map them. Option C is wrong as Alex's conclusion is incorrect.

Answer:

A. The circles are mapped onto each other, so they are congruent.