Question

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

Explanation:

Step1: Analyze rigid - motion properties

Rigid motions include translations, rotations, and reflections. Congruent triangles can be mapped onto each other using rigid motions.

Step2: Examine the orientation of triangles

By observing the orientation of \(\triangle IJK\) and \(\triangle LJM\), we can see that there is no rotation or reflection that can map \(\triangle IJK\) onto \(\triangle LJM\) exactly. The relative positions and orientations of the sides and angles do not match in a way that would allow for a rigid - motion mapping.

Answer:

No. It is not possible to map \(\triangle IJK\) onto \(\triangle LJM\) using only rigid motions.