Question

if a series of rigid transformations maps $\triangle qrs$ onto $\triangle mpn$, match each side of triangle $mpn$ with its length
(image of $\triangle qrs$ with $rq = 8$, $qs = 6$, $rs = 7$)

Explanation:

Step1: Recall Rigid Transformations

Rigid transformations (translation, rotation, reflection) preserve the side lengths of a figure. So, $\triangle QRS \cong \triangle MPN$, meaning corresponding sides are equal.

Step2: Identify Corresponding Sides

In $\triangle QRS$, sides are $QR = 8$, $RS = 7$, $QS = 6$. So in $\triangle MPN$, the sides will match these lengths. If we assume the correspondence (e.g., $QR$ corresponds to a side in $MPN$, $RS$ to another, $QS$ to the third), the lengths remain 8, 7, 6.

Answer:

The side lengths of $\triangle MPN$ are 8, 7, and 6 (matching the side lengths of $\triangle QRS$ due to rigid transformations preserving length).