Question

practice using the sas congruence theorem. which rigid transformations would map \\( \triangle jkl \\) onto \\( \triangle pqr \\)? 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:

• A reflection only: If we reflect \(\triangle{JKL}\) over a line (not just any line, but a specific one that aligns the triangles), it can map \(\triangle{JKL}\) onto \(\triangle{PQR}\).
• A rotation and a reflection: First, rotate \(\triangle{JKL}\) to get it in a better orientation and then reflect it to map onto \(\triangle{PQR}\).
• A translation and a reflection: Translate \(\triangle{JKL}\) (move it without rotation or reflection first) and then reflect it to make it coincide with \(\triangle{PQR}\).

A rotation only or a translation only cannot map \(\triangle{JKL}\) onto \(\triangle{PQR}\) because their orientations (for rotation only) or positions (for translation only) are not such that a single rotation or translation can achieve the congruence.

Answer:

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