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: Analyze Congruence

Both triangles have two sides (16 cm, 24 cm) and the included right angle, so they are congruent by SAS. So options saying they are not congruent or can't be mapped are wrong.

Step2: Evaluate Transformations

• Option 3: Translating R to B, then rotating S to C. But the right angle vertex in ΔQRS is R, in ΔABC is B. After translation R→B, rotating S to C: check the angle. The right angle in ΔQRS is at R, in ΔABC at B. Rotating after translation should align, but let's check option 4.
• Option 4: Translate Q→A, then reflect over QS. Translating Q to A, then reflecting over QS (which is a horizontal line, maybe) would flip the triangle to match ΔABC's orientation (right angle at B, similar to ΔQRS's right angle at R, but reflection can adjust orientation). Since they are congruent, rigid transformations (translation, reflection, rotation) can map them. Option 4's transformation is valid.

Answer:

Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing $\overline{QS}$ (the fourth option).