Question

how can δabc be mapped to δxyz? first, translate ______________. next, rotate δabc about b to align the sides and angles. 25 cm b 36° a 29 cm c y z 25 cm 36° 29 cm x vertex b to vertex z vertex b to vertex y vertex a to vertex z vertex a to vertex y

Explanation:

To map \(\triangle ABC\) to \(\triangle XYZ\), we need to match corresponding vertices. In \(\triangle ABC\), side \(AB = 25\) cm and in \(\triangle XYZ\), side \(XY=25\) cm. Also, \(\angle A = 36^{\circ}\) and \(\angle X = 36^{\circ}\). So, vertex \(A\) should be mapped to vertex \(X\) first. But looking at the options, we note that after translation and rotation (about \(B\)), we want to align the triangles. Since \(AB = XY = 25\) cm and we rotate about \(B\), we first translate vertex \(A\) to vertex \(Y\) (because if we consider the structure of the triangles, after translating \(A\) to \(Y\) and then rotating about \(B\) (which will be adjusted in position relative to the new position of \(A\) (now \(Y\))), we can align the sides and angles of the two triangles.

Answer:

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