Question

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

Explanation:

Step1: Identify side - length correspondence

In \(\triangle EFG\), \(EF = 4.5\)m, \(FG=3\)m, \(EG = 5\)m. In \(\triangle HIG\), \(HI=4.5\)m, \(IG = 3\)m, \(HG=5\)m. The side - lengths are equal: \(EF = HI\), \(FG=IG\), \(EG = HG\).

Step2: Analyze rigid motions

A reflection can be used to map \(\triangle EFG\) onto \(\triangle HIG\). We can find a line of reflection such that the points of \(\triangle EFG\) are mapped to the corresponding points of \(\triangle HIG\) because the corresponding sides are equal. A rotation alone will not map \(\triangle EFG\) onto \(\triangle HIG\) as the orientation and position require a flip (reflection).

Answer:

Yes. A reflection can map \(\triangle EFG\) onto \(\triangle HIG\).