Question

helena was curious if quadrilaterals qrst and x y zw were congruent, so she tried to map one figure onto the other using transformations: helena concluded: \its not possible to map qrst onto x y zw using a sequence of rigid transformations, so the quadrilaterals are not congruent.\ what error did helena make in her conclusion? choose 1 answer: a one more transformation — a rotation — would map qrst onto x y zw. so the quadrilaterals are congruent. b one more transformation — a reflection — would map qrst onto x y zw. so the quadrilaterals are congruent. c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Helena's conclusion, we analyze rigid transformations (translations, rotations, reflections) that preserve congruence. The figures likely require a rotation (a rigid transformation) to map one onto the other. Option A states a rotation would map QRST to X Y Z W, meaning they are congruent, so Helena's error was not considering this rotation. Option B's reflection is less likely, and C is incorrect as there is an error.

Answer:

A. One more transformation — a rotation — would map \( QRST \) onto \( X Y Z W \). So the quadrilaterals are congruent.