how can a translation and a rotation be used to map δhjk to δlmn?
- translate h to l and rotate about h until $\overline{hk}$ lies on the line containing $\overline{lm}$.
- translate k to m and rotate about k until $\overline{hk}$ lies on the line containing $\overline{lm}$.
- translate k to n and rotate about k until $\overline{hk}$ lies on the line containing $\overline{ln}$.
- translate h to n and rotate about h until $\overline{hk}$ lies on the line containing $\overline{ln}$.

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# Brief Explanations:
To map $\triangle HJK$ to $\triangle LMN$, we analyze the congruent sides (marked with tick marks) and corresponding vertices. First, translate $K$ to $N$ (since $HK$ and $LN$ are corresponding sides with the same tick - mark pattern, and $K$ and $N$ should align). Then, rotate about $K$ (now at $N$) until $\overline{HK}$ lies on the line containing $\overline{LN}$. Let's check the other options:
- Option 1: Translating $H$ to $L$ and rotating about $H$ won't align the sides correctly as the corresponding sides involving $K$ and $N$ are not considered.
- Option 2: Translating $K$ to $M$ is incorrect because $K$ should correspond to $N$ (from the tick - mark - ed sides), not $M$.
- Option 4: Translating $H$ to $N$ and rotating about $H$ is incorrect as the translation should align $K$ with $N$ first.

# Answer:
C. Translate $K$ to $N$ and rotate about $K$ until $\overline{HK}$ lies on the line containing $\overline{LN}$

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