Final answer:
To map congruent quadrilateral WXYZ to WTUV, one can use a composition of rigid motions such as translation, rotation, and possibly reflection. These steps are congruence-preserving transformations that can align one figure with the other precisely without altering their size or shape.
Step-by-step explanation:
To describe a composition of rigid motions that maps quadrilateral WXYZ to quadrilateral WTUV, given that they are congruent, we should first consider the properties of rigid motions. Rigid motions, also known as isometries, include translations, rotations, and reflections, and they preserve the size and shape of geometric figures. In the context of rigid motions, quadrilaterals WXYZ and WTUV being congruent means there is a sequence of such motions that will map one onto the other exactly.
One potential composition of rigid motions could start with a translation, where you slide WXYZ in a straight line so that one of its vertices, say W, overlaps with vertex W of WTUV. Once the vertices are coincident, a rotation around that vertex may be necessary to align the edges. If a reflection is required, for instance, if quadrilateral WXYZ is a mirror image of WTUV, the final step would be to reflect WXYZ over the appropriate line of symmetry, achieving congruence with WTUV. If no reflection is necessary, then the composition would be complete after translation and rotation.
It is also possible that a single rotation around the correct point and through the proper angle could align WXYZ with WTUV if no translation is needed. Alternatively, WTUV could be the mirrored image of WXYZ along a certain axis, leading with a reflection followed by rotation or translation if necessary. Each of these step-by-step processes is a valid composition of rigid motions that can transform WXYZ to overlay WTUV perfectly.