Question

is △efg congruent to △hig? justify your answer using rigid motions.
yes. a rotation can map △efg onto △hig.
yes. a reflection can map △efg onto △hig.
no. it is not possible to map △efg onto △hig using only rigid motions.

Explanation:

Step1: Identify corresponding sides

We have $EF = 4.5$ m, $FG=3$ m, $EG = 5$ m, $HI = 4.5$ m, $IG = 3$ m, $HG=5$ m. So $EF = HI$, $FG=IG$, $EG = HG$.

Step2: Consider rigid - motions

Rigid motions include translations, rotations, and reflections. Since the corresponding sides of $\triangle EFG$ and $\triangle HIG$ are equal, we can map $\triangle EFG$ onto $\triangle HIG$ using a reflection. A reflection across the line that bisects $\angle FGI$ will map $\triangle EFG$ onto $\triangle HIG$.

Answer:

Yes. A reflection can map $\triangle EFG$ onto $\triangle HIG$.