Question

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

Explanation:

Step1: Recall rigid - motion properties

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures.

Step2: Compare side - lengths

In \(\triangle EIX\), the side - lengths are \(EI = 52m\), \(IX = 28m\), \(EX=60m\). In \(\triangle AOX\), the side - lengths are \(AO = 39m\), \(OX = 21m\), \(AX = 45m\). Since \(52
eq39\), \(28
eq21\), \(60
eq45\), the side - lengths are not equal.

Step3: Determine congruence

Since rigid motions preserve side - lengths and the side - lengths of \(\triangle EIX\) and \(\triangle AOX\) are not equal, it is not possible to map \(\triangle EIX\) onto \(\triangle AOX\) using only rigid motions.

Answer:

No. It is not possible to map \(\triangle EIX\) onto \(\triangle AOX\) using only rigid motions.