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 $\overline{db}$, 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 $\overline{fc}$.
choose 1 answer:

Explanation:

Step1: Analyze Sequence A

First, translate $\triangle DEF$ along $\overline{DB}$. This moves point $D$ to $B$. Then, rotate $90^\circ$ about $B$. Check if this aligns $\triangle DEF$ with $\triangle ABC$. The orientation and position after translation and rotation should match.

Step2: Analyze Sequence B

Rotate $\triangle DEF$ $90^\circ$ about $F$, then translate along $\overline{FC}$. The rotation about $F$ would change the orientation, and subsequent translation may not align with $\triangle ABC$ as well as Sequence A.

Step3: Compare Sequences

Sequence A: Translation to move $D$ to $B$, then rotation about $B$ adjusts the angle to match $\triangle ABC$'s orientation. Sequence B's rotation about $F$ and translation doesn't align the triangles correctly.

Answer:

Sequence A (A translation along the directed line segment $\overline{DB}$, then a $90^\circ$ rotation about point $B$)