which of these triangle pairs can be mapped to each other using both a translation and a reflection across…

which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing ab?

which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing ab?

Answer

Explanation:

Step1: Recall transformation rules

Translation moves a figure and reflection flips it over a line.

Step2: Analyze each pair

For a pair to be mapped by translation and reflection across line containing $\overline{AB}$, corresponding sides and angles must match. In the first - pair, we can first translate $\triangle XYZ$ so that a point (say $Y$) coincides with a corresponding point on $\triangle ABC$. Then, reflecting across the line containing $\overline{AB}$ can map the two triangles onto each other as the sides and angles are congruent and in the right orientation for such a transformation.

Answer:

The first pair of triangles.