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

The side - lengths of $\triangle QRS$ are $QR = 16$ cm, $RS=24$ cm and $\angle R = 90^{\circ}$, and for $\triangle ABC$, $AB = 16$ cm, $BC = 24$ cm and $\angle B=90^{\circ}$. By the Side - Angle - Side (SAS) congruence criterion, $\triangle QRS\cong\triangle ABC$.

Step2: Analyze rigid transformations

Rigid transformations include translations, rotations and reflections. If we first translate $\triangle QRS$ so that $Q$ is mapped to $A$ (a translation moves the entire figure without changing its shape or size), and then reflect $\triangle QRS$ across the line containing $QS$, we can map $\triangle QRS$ to $\triangle ABC$.

Answer:

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