Question

triangles $\triangle def$ and $\triangle abc$ are congruent.

which of the following sequences of transformations maps $\triangle def$ onto $\triangle abc$

sequence a
a translation along the directed line segment $db$, then a $90^{\circ}$ rotation about point $b$

sequence b
a $90^{\circ}$ rotation about point $f$, then a translation along the directed line segment $fc$

choose 1 answer.

$\bigcirc$ only sequence a

$\bigcirc$ only sequence b

$\bigcirc$ both

$\bigcirc$ neither

Explanation:

Step1: Analyze Sequence A

First, translate $\triangle DEF$ along $\overrightarrow{DB}$. This moves $D$ to $B$. Then, rotate $90^\circ$ about $B$. Since $\triangle DEF \cong \triangle ABC$, the rotation will align the sides and angles correctly to map $\triangle DEF$ to $\triangle ABC$.

Step2: Analyze Sequence B

Rotate $\triangle DEF$ $90^\circ$ about $F$. Then translate along $\overrightarrow{FC}$. After rotation, the translation will not align $\triangle DEF$ to $\triangle ABC$ correctly because the rotation about $F$ and subsequent translation doesn't match the congruent triangle's orientation and position as well as Sequence A. So only Sequence A works.

Answer:

A. Only sequence A