Question

is △efg congruent to △uvw? justify your answer using rigid motions.
yes. a rotation and a reflection can map △efg onto △uvw.
yes. a translation and a rotation can map △efg onto △uvw.
no. it is not possible to map △efg onto △uvw using only rigid motions.

Explanation:

Step1: Analyze the side - angle - side (SAS) congruence

In \(\triangle EFG\) and \(\triangle UVW\), we have \(FG = VW=12\mathrm{cm}\), \(\angle G=\angle V\), \(GE = VU = 16\mathrm{cm}\). By the SAS (side - angle - side) congruence criterion, \(\triangle EFG\cong\triangle UVW\).

Step2: Consider rigid motions

Rigid motions (translation, rotation, reflection) preserve the shape and size of a figure. A translation moves the triangle without rotation or reflection. A rotation can be used to align the angles. Since \(\triangle EFG\) and \(\triangle UVW\) are congruent (by SAS), a translation and a rotation can map \(\triangle EFG\) onto \(\triangle UVW\).

Answer:

Yes. A translation and a rotation can map \(\triangle EFG\) onto \(\triangle UVW\).