Question

is there a series of rigid transformations that could map δqrs to δabc? if so, which transformations could be used? no, δqrs and δabc are congruent but δqrs cannot be mapped to δabc using a series rigid transformations. no, δqrs and δabc are not congruent. yes, δqrs can be translated so that r is mapped to b and then rotated so that s is mapped to c. yes, δqrs can be translated so that q is mapped to a and then reflected across the line containing qs.

Explanation:

Step1: Check congruence

Since $QR = AB=16$ cm and $RS = BC = 24$ cm and the included - angle $\angle R=\angle B = 90^{\circ}$, by the Side - Angle - Side (SAS) congruence criterion, $\triangle QRS\cong\triangle ABC$.

Step2: Analyze rigid transformations

A translation can be used to move $\triangle QRS$ so that a corresponding vertex (e.g., $Q$) is mapped to its corresponding vertex ($A$) in $\triangle ABC$. Then, a reflection across the line containing the common side (or an appropriate line) can be used to map the other vertices correctly.

Answer:

Yes, $\triangle QRS$ can be translated so that $Q$ is mapped to $A$ and then reflected across the line containing $\overline{QS}$.