Question

kl and no are parallel. m is the midpoint of segment ko. what transformation can be used to prove that ∠m ≅ ∠n?

Explanation:

Step1: Recall the property of rotation

A rotation about the mid - point \(M\) of \( \overline{KO}\) can be considered.
Since \(M\) is the mid - point of \( \overline{KO}\), \(KM = MO\).
When we rotate \( \triangle KML\) about point \(M\) by \(180^{\circ}\), the segment \( \overline{KM}\) maps to \( \overline{MO}\) (because \(KM = MO\)).

Step2: Use the parallel lines property

Because \( \overline{KL}\parallel\overline{NO}\), the rotation will map \( \angle m\) to \( \angle n\). A \(180^{\circ}\) rotation about the mid - point \(M\) of \( \overline{KO}\) is a transformation that maps \( \overline{KL}\) to \( \overline{NO}\) (due to parallelism and mid - point property) and \( \angle m\) to \( \angle n\).

Answer:

A \(180^{\circ}\) rotation about point \(M\) (the mid - point of \( \overline{KO}\)) can be used to prove that \( \angle m\cong\angle n\).