Question

how can δabc be mapped to δxyz? first, translate vertex a to vertex dropdown. next, dropdown δabc to align the sides and angles.

Explanation:

Step1: Identify Corresponding Vertex

In triangle \( \triangle ABC \), vertex \( A \) has sides \( AB = 28 \, \text{cm} \) and \( AC = 32 \, \text{cm} \). In triangle \( \triangle XYZ \), vertex \( X \) has sides \( XY = 28 \, \text{cm} \) and \( XZ = 32 \, \text{cm} \). So, translate vertex \( A \) to vertex \( X \).

Step2: Determine Transformation to Align

After translating \( A \) to \( X \), we need to rotate \( \triangle ABC \) to align the sides and angles because the orientation of the triangles (the angle between the sides) needs to match. Rotation will adjust the position of \( B \) and \( C \) to match \( Y \) and \( Z \) respectively.

Answer:

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