Final answer:
A sequence of translations and reflections, which are rigid motions, preserves both angle measures and segment lengths in a geometric figure.
This correct answer is c)
Step-by-step explanation:
The sequence of transformations described involves a translation, a reflection over line PQ, and another reflection over line RS. Under these sequence of transformations, certain properties of geometric figures are preserved.
Translations and reflections are both rigid motions, which means that they do not alter the size and shape of a geometric figure. Therefore, the answer to what must be preserved under this sequence of transformations is both angle measures and segment lengths.
For translations, objects are moved without rotation or reflection, meaning that all corresponding angles and sides remain congruent with their pre-image.
For reflections, figures are flipped over a line, which also preserves the congruency of angles and lengths of segments.
Although the orientation of the figure changes after reflection, the angle measures and segment lengths do not change. This means that under the sequence of translations and reflections, c) Both angle measures and segment lengths are preserved.
This correct answer is c)