Final answer:
To map triangle ABC onto XYZ, one would likely need to perform a translation, a rotation, and possibly a reflection. The exact rigid transformations depend on the orientation and congruence of the other sides of the triangles.
Step-by-step explanation:
The student is asking about mapping one triangle onto another using rigid transformations. In mathematics, a rigid transformation involves moving a shape without altering its size or shape. For triangles ABC and XYZ, given that side AC is congruent to side ZX, angles BAC and ZXY are both 35 degrees, angle XYZ is 47 degrees, and angle ABC is 98 degrees, we can determine the necessary transformations.
First, we notice that the two triangles have one pair of corresponding congruent sides and one pair of corresponding congruent angles. This suggests that we can map triangle ABC onto XYZ using a series of rigid transformations. Since the sides AC and ZX are congruent, we would start with a translation that moves vertex A to vertex Z. Following that, because angles BAC and ZXY are congruent, we would perform a rotation about vertex Z to align side AC with side ZX. Finally, if necessary, we could apply a reflection across the appropriate line that passes through Z if the orientation of the triangles requires it to match completely.
Considering the given angles, the rotation required would likely be the difference in the measures of angles ABC and XYZ (these would be supplementary if angle ABC is 98 degrees and XYZ is 47 degrees, as the third angles of each triangle would also have to be congruent for the triangles to be congruent). However, to completely determine the necessary rigid transformations, additional information about the orientation and congruence of the other sides would be necessary.