Question

determine the rigid transformations that will map △abc to △xyz. translate vertex x to vertex c; rotate △xyz to align the sides and angles. translate vertex x to vertex a; rotate △xyz to align the sides and angles. translate vertex b to vertex z; reflect △abc across side ab. reflect △abc across side ab; translate vertex c to vertex x.

Explanation:

Step1: Match corresponding vertices

Vertices with equal - angle measures and side - length relationships should be matched. In \(\triangle ABC\) and \(\triangle XYZ\), \(\angle A = 35^{\circ}\) and \(\angle Z=47^{\circ}\), \(\angle B = 98^{\circ}\), and the side - length marked on \(AC\) and \(ZX\) are equal. We should first match the vertices with equal - angle or side - length features. Vertex \(A\) and vertex \(X\) have equal - angle measures in their respective triangles related to the marked sides.

Step2: Determine transformation

The first step of rigid transformation is translation. We need to translate vertex \(X\) to vertex \(A\). After translation, we need to rotate \(\triangle XYZ\) to align the sides and angles of \(\triangle ABC\) and \(\triangle XYZ\).

Answer:

Translate vertex \(X\) to vertex \(A\); rotate \(\triangle XYZ\) to align the sides and angles.