Question

△jkl is congruent to △jkl because you can map △jkl to △jkl using a translation 5 units up, which is a rigid motion
△jkl is not congruent to △jkl because there is no sequence of rigid motion that maps △jkl to △jkl
△jkl is congruent to △jkl because you can map △jkl to △jkl using a reflection across the x - axis, which is a rigid motion
△jkl is congruent to △jkl because you can map △jkl to △jkl using a rotation of 90 degrees counterclockwise about the origin, which is a rigid motion

Explanation:

Step1: Recall rigid - motion properties

Rigid motions (translations, reflections, rotations) preserve congruence.

Step2: Analyze translation

If we translate $\triangle{JKL}$ 5 units up, the orientation of the triangles will not match.

Step3: Analyze reflection across x - axis

If we reflect $\triangle{JKL}$ across the x - axis, the orientation will be wrong.

Step4: Analyze rotation

A 90 - degree counter - clockwise rotation about the origin maps $\triangle{JKL}$ to $\triangle{J'K'L'}$. For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$.

Answer:

$\triangle{JKL}$ is congruent to $\triangle{J'K'L'}$ because you can map $\triangle{JKL}$ to $\triangle{J'K'L'}$ using a rotation of 90 degrees counterclockwise about the origin, which is a rigid motion.