Question

which rigid transformations would map △jkl onto △pqk? select the three correct answers.
□ a reflection only
□ a rotation only
□ a rotation and a reflection
□ a translation and a reflection
□ a translation only

Explanation:

1. Reflection only: A reflection over the appropriate line (e.g., the angle bisector or a line of symmetry) could map \(\triangle JKL\) to \(\triangle PQR\) if the triangles are mirror - images with respect to that line. The marked congruent sides and angles suggest that a reflection could align the corresponding parts.
2. Rotation and a reflection: First, a rotation about point \(K\) (or another center) can align the triangles in a certain orientation, and then a reflection can further adjust the position to make them coincide. The congruent sides and angles (marked with ticks and arcs) are consistent with a combination of rotation and reflection.
3. Translation and a reflection: A translation can move \(\triangle JKL\) to a position near \(\triangle PQR\), and then a reflection can flip it to match the orientation of \(\triangle PQR\). The congruent side lengths and angle measures support this combination of transformations.

• A rotation only is not sufficient because the orientation of the triangles (the way the sides and angles are arranged) might not be aligned just by rotation. A translation only is also not sufficient as the orientation (the "flip" or "turn" aspect) of the triangles is different, and just moving them (translation) won't make them coincide.

Answer:

a reflection only, a rotation and a reflection, a translation and a reflection