Question

is \\( \triangle bcd \\) congruent to \\( \triangle wxy \\)? justify your answer using rigid motions.
yes. a reflection can map \\( \triangle bcd \\) onto \\( \triangle wxy \\).
yes. a translation and a rotation can map \\( \triangle bcd \\) onto \\( \triangle wxy \\).
no. it is not possible to map \\( \triangle bcd \\) onto \\( \triangle wxy \\) using only rigid motions.

Explanation:

Step1: Check the ratios of corresponding sides

For \(\triangle BCD\) and \(\triangle WXY\), we have \(\frac{BC}{WX}=\frac{5}{7}\), \(\frac{CD}{XY}=\frac{12}{16.8}=\frac{120}{168}=\frac{5}{7}\), \(\frac{BD}{WY}=\frac{13}{18.2}=\frac{130}{182}=\frac{5}{7}\)

Step2: Analyze rigid - motion implications

Since the ratios of corresponding sides are equal (\(\triangle BCD\sim\triangle WXY\) with a scale factor of \(\frac{5}{7}\)), but rigid motions (translation, rotation, reflection) preserve side - lengths. In a similarity with a scale factor not equal to \(1\), we cannot map one triangle onto the other using only rigid motions.

Answer:

No. It is not possible to map \(\triangle BCD\) onto \(\triangle WXY\) using only rigid motions.