Question

how can △abc be mapped to △xyz? first, translate ______________. next, rotate △abc about b to align the sides and angles. vertex a to vertex y vertex b to vertex z vertex a to vertex z vertex b to vertex y

Explanation:

Step1: Analyze the correspondence of vertices

In congruent triangles, we need to match corresponding vertices. Looking at the side - angle - side (SAS) congruence (since \(AB = XY=25\space cm\), \(\angle A=\angle X = 36^{\circ}\), \(AC = XZ = 29\space cm\)), vertex \(A\) should correspond to vertex \(X\), but if we consider the translation - rotation mapping.

If we want to map \(\triangle ABC\) to \(\triangle XYZ\) using translation and rotation:
We know that in the translation - rotation sequence, we first try to match one of the vertices.
Since \(AB = XY\) and we want to use a translation followed by a rotation about \(B\).
We note that if we translate vertex \(A\) to vertex \(Y\), then after translation, when we rotate \(\triangle ABC\) about \(B\), we can align the sides and angles.

Answer:

vertex \(A\) to vertex \(Y\)