Question

determining 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.
(diagrams of △abc and △xyz with side lengths 32 cm, 28 cm and marked angles at a and x)

Explanation:

Step1: Analyze Vertex Alignment

To map \( \triangle ABC \) to \( \triangle XYZ \), first translate vertex \( A \) to vertex \( X \) (since corresponding vertices should align, and \( A \) corresponds to \( X \) as they have the same angle and side lengths).

Step2: Determine Next Transformation

After translating \( A \) to \( X \), we need to rotate \( \triangle ABC \) (around \( X \)) to align the sides and angles. The sides \( AX \) (after translation) will have \( AB = XY = 28 \, \text{cm} \) and \( AC = XZ = 32 \, \text{cm} \), so a rotation will align the remaining vertices \( B \) and \( C \) to \( Y \) and \( Z \) respectively.

Answer:

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