Question

etermining a combination of rigid transformations
how can △abc be mapped to △xyz?
first, translate vertex a to vertex
next △abc to align the sides and angles.
translate
reflect
rotate

Explanation:

Step1: Analyze the triangles

We have two triangles \(\triangle ABC\) and \(\triangle XYZ\). In \(\triangle ABC\), side \(AB = 28\) cm, side \(AC=32\) cm. In \(\triangle XYZ\), side \(XY = 28\) cm, side \(XZ = 32\) cm. The angle in \(\triangle ABC\) at \(A\) and the angle in \(\triangle XYZ\) at \(X\) are the included angles between the pairs of sides (\(AB - AC\) and \(XY - XZ\) respectively).

Step2: Determine the first transformation

To map \(\triangle ABC\) to \(\triangle XYZ\), we first need to translate vertex \(A\) to vertex \(X\). This is because the sides adjacent to \(A\) (\(AB = 28\) cm and \(AC = 32\) cm) correspond to the sides adjacent to \(X\) (\(XY = 28\) cm and \(XZ = 32\) cm).

Step3: Determine the second transformation

After translating \(A\) to \(X\), we need to rotate \(\triangle ABC\). Rotation is a rigid transformation that can be used to align the sides and angles. A translation just moves the figure, a reflection would flip the figure (which is not needed here as the orientation of the triangles can be made to match with a rotation).

Answer:

First, translate vertex \(A\) to vertex \(X\). Next, rotate \(\triangle ABC\) to align the sides and angles.