Question

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

Explanation:

Step1: Identify corresponding sides and angles

In $\triangle EFG$, sides are $EF = 18$m, $EG=12$m, $FG = 7$m and in $\triangle JKL$, sides are $JK = 18$m, $JL = 12$m, $KL=7$m. Also, corresponding angles are equal in measure as shown by the arc - markings.

Step2: Analyze rigid - motions

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. Since $\triangle EFG$ and $\triangle JKL$ have the same side - lengths and angle - measures, we can use a reflection to map $\triangle EFG$ onto $\triangle JKL$. The orientation of the two triangles suggests a reflection across a vertical line between them.

Answer:

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