Question

describe the sequence of rigid motions that was used to take each vertex of triangle abc onto the corresponding vertex of triangle def. translate triangle abc by the directed line segment . then reflect the resulting image across segment

Explanation:

Step1: Identify translation

To move triangle ABC to a position relative to triangle DEF, first, we need to translate it so that one of the vertices aligns. By observing, we can translate triangle ABC by the directed line segment $\overrightarrow{AC'}$. This will move point A to point C'.

Step2: Identify reflection

After translation, we need to reflect the translated - triangle across a line to match it with triangle DEF. The line of reflection is the perpendicular bisector of the segment joining a corresponding pair of non - aligned vertices. In this case, reflecting across segment DF will map the translated triangle onto triangle DEF.

Answer:

Translate triangle ABC by the directed line segment $\overrightarrow{AC'}$. Then reflect the resulting image across segment DF.