Question

triangle congruence: sas
how can a translation and a rotation be used to map △hjk to △lmn?
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}).
translate h to l and rotate about h until (overline{hk}) lies on the line containing (overline{lm}).

Explanation:

Step1: Analyze translation

Translation moves a figure without rotation. To map \( \triangle HJK\) to \( \triangle LMN\), we first translate \(H\) to \(L\) (as \(H\) and \(L\) are corresponding vertices in the congruent triangles).

Step2: Analyze rotation

After translating \(H\) to \(L\), we rotate about \(H\) (now at \(L\)) so that \( \overline{HK}\) lies on the line containing \( \overline{LM}\) (since in congruent triangles \( \triangle HJK\cong\triangle LMN\) by SAS, the sides and angles must align).

Answer:

Translate \(H\) to \(L\) and rotate about \(H\) until \( \overline{HK}\) lies on the line containing \( \overline{LM}\).