Question

casey was able to map line segment \\( \overline{uv} \\) onto line segment \\( \overline{st} \\) using a translation and a rotation.

casey concluded:

\i was able to map line segment \\( \overline{uv} \\) onto line segment \\( \overline{st} \\) using a sequence of rigid transformations without a dilation, so the figures are congruent but they are not similar.\

what error did casey make in her conclusion?

choose 1 answer:

\\( \bigcirc \\) a the correct conclusion is that the segments are congruent and similar.

\\( \bigcirc \\) b the correct conclusion is that the segments are neither congruent, nor similar.

\\( \bigcirc \\) c there is no error. this is a correct conclusion.

Explanation:

Congruent figures are a special case of similar figures. When two figures are congruent (mapped via rigid transformations like translation and rotation, which preserve shape and size), they are also similar (same shape, ratio of corresponding sides is \(1\)). Casey wrongly thought congruent and similar are mutually - exclusive.

Answer:

A. The correct conclusion is that the segments are congruent and similar.