Question

how can △wxy be mapped to △mnq?
translate vertex w to vertex m, then reflect across the line containing
__________

Explanation:

Step1: Analyze the triangles

We know that for triangle congruence (here likely using SAS - Side - Angle - Side), we need to match the corresponding sides and angles.

Step2: Match the sides

In \(\triangle WXY\) and \(\triangle MNQ\), \(WX = MN=18\mathrm{cm}\), \(WY = MQ = 30\mathrm{cm}\), and the included angles at \(W\) and \(M\) are equal.

Step3: Determine the reflection line

After translating vertex \(W\) to vertex \(M\), we need to reflect \(\triangle WXY\) across the line that will make the sides and angles match. Since \(WY\) corresponds to \(MQ\) and \(WX\) corresponds to \(MN\), the line of reflection should be the line that will align the sides. If we consider the side - angle - side congruence, when we translate \(W\) to \(M\), reflecting across the line containing \(\overline{XY}\) (because after translation, \(\overline{XY}\) will align with \(\overline{NQ}\) to complete the SAS mapping)

Answer:

\(\overline{XY}\)