Question

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

Explanation:

Step1: Check congruence by S - A - S

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

Step2: Analyze rigid - transformations

A translation can be used to move $\triangle QRS$ so that point $Q$ is mapped to point $A$. Then, a reflection across the line containing $\overline{QS}$ can be used to map the remaining points correctly.

Answer:

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