Question

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

Explanation:

Step1: Analyze angle - side - angle (ASA)

In $\triangle GHI$, angles are $34^{\circ},34^{\circ},112^{\circ}$. In $\triangle JKL$, angles are $56^{\circ},56^{\circ},68^{\circ}$. The side - angle - side relationships are different.

Step2: Consider rigid motions

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. Since the angle - side - angle combinations of the two triangles are not the same, we cannot map one onto the other using rigid motions.

Answer:

No. It is not possible to map $\triangle GHI$ onto $\triangle JKL$ using only rigid motions.