Question

which rigid transformation would map δaqr to δakp?
○ a rotation about point a
○ a reflection across the line containing (overline{ar})
○ a reflection across the line containing (overline{aq})
○ a rotation about point r

Explanation:

To determine the rigid transformation mapping \( \triangle AQR \) to \( \triangle AKP \), we analyze the given diagram. A rigid transformation preserves shape and size. Looking at the triangles, the common vertex is \( A \). A rotation about point \( A \) would align the corresponding sides and angles. The marked congruent segments and angles suggest that rotating \( \triangle AQR \) around \( A \) (such that \( AQ \) maps to \( AK \) and \( AR \) maps to \( AP \)) would map \( \triangle AQR \) to \( \triangle AKP \). Reflections across \( \overline{AR} \) or \( \overline{AQ} \) would not align the triangles as needed, and rotation about \( R \) is incorrect since \( R \) is not the center of symmetry here.

Answer:

a rotation about point A