Question

determining a combination of rigid transformations
how can δabc be mapped to δxyz?
first, translate vertex a to vertex
next, δabc to align the sides and angles.

Explanation:

Step1: Analyze corresponding vertices

In $\triangle ABC$, vertex $A$ has sides $AB = 28$ cm and $AC = 32$ cm with the included angle. In $\triangle XYZ$, vertex $X$ has sides $XY = 28$ cm and $XZ = 32$ cm with the included angle. So, we translate vertex $A$ to vertex $X$ to start aligning the triangles.

Step2: Determine the next transformation

After translating $A$ to $X$, we need to rotate $\triangle ABC$ (around point $X$) to align the sides and angles because the orientation of the sides relative to the angle might be different, and rotation is a rigid transformation that can adjust the orientation to match $\triangle XYZ$.

Answer:

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