Question

triangle congruence
how can a translation and a reflection be used to map △hjk to △lmn?
translate k to n and reflect across the line containing $overline{hj}$.
translate k to n and reflect across the line containing $overline{jk}$.
translate k to l and reflect across the line containing $overline{hj}$.
translate h to l and reflect across the line containing $overline{jk}$.

Explanation:

Step1: Analyze translation

Translation is a transformation that slides a figure. We want to map \(\triangle HJK\) to \(\triangle LMN\). Looking at the vertices, we should first translate vertex \(K\) to vertex \(N\) since they are corresponding vertices (by the congruence of the triangles).

Step2: Analyze reflection

After translating \(K\) to \(N\), we need to reflect. The side \(JK\) in \(\triangle HJK\) corresponds to \(MN\) in \(\triangle LMN\). When we translate \(K\) to \(N\), the line of reflection should be the line containing \(JK\) (because after translation of \(K\) to \(N\), reflecting across the line containing \(JK\) will map the translated \(\triangle HJK\) to \(\triangle LMN\))

Answer:

Translate \(K\) to \(N\) and reflect across the line containing \(\overline{JK}\)