A composition of translation and rotation maps DE to JK with angle D corresponding to angle J. However, congruence of EF to KL is not guaranteed and depends on additional considerations of angles and side lengths.
To map triangle DE to triangle JK such that angle D corresponds to angle J, and DE corresponds to JK, a composition of rigid motions involving translation and rotation can be employed. First, a translation is applied to move DE to align with JK. Following the translation, a rotation is performed to ensure that angle D is congruent to angle J. These rigid motions maintain the shape and size of the triangles while repositioning and orienting them in space.
Now, since angle D is congruent to angle J and DE is congruent to JK, it follows that the composition of rigid motions maps triangle DE to triangle JK as specified.
However, when considering the mapping of EF to KL, it's important to note that the rigid motions mentioned earlier do not guarantee the congruence of EF to KL. The rotation involved in mapping D to J may alter the orientation of EF relative to KL. To determine whether EF is congruent to KL, additional information about the angles and sides of the triangles is needed.
In summary, a composition of translation and rotation can accurately map DE to JK with angle D corresponding to angle J. However, the congruence of EF to KL is not assured by the same rigid motions and would require additional considerations of angles and side lengths.