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) and can be mapped onto each other via translations, rotations, or reflections. Since Circles A and B coincide (their centers are very close, and the circle appears to have the same radius), they can be mapped onto each other, meaning they are congruent. Alex incorrectly focused on sides/angles (circles have neither sides nor angles in the traditional polygon sense) and concluded they aren't congruent. Option A correctly states that the circles are mapped onto each other (hence congruent), identifying Alex's error. Option B is wrong because congruence of circles depends on radius, not requiring a transformation to be applied, and Option C is wrong as Alex's conclusion is incorrect.

Answer:

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