Question

1. polygon hijkl is a reflection and translation of polygon gfonm. is segment kj congruent to segment nm? choose: yes! explain your reasoning. no! name the angle that is congruent to segment nm.

Explanation:

Step1: Properties of reflection and translation

Reflection and translation are rigid transformations. Rigid transformations preserve the shape and size of a figure. That is, if polygon \(HIJKL\) is a reflection and translation of polygon \(GFONM\), then the two polygons are congruent (\(HIJKL\cong GFONM\)).

Step2: Corresponding parts of congruent polygons

For congruent polygons, corresponding sides are congruent. When we consider the correspondence of the vertices: \(G\to H\), \(F\to I\), \(O\to J\), \(N\to K\), \(M\to L\). So, the side \(NM\) in polygon \(GFONM\) corresponds to the side \(KL\) in polygon \(HIJKL\) (by the order of the vertices in the congruent polygons).

Answer:

NO! The segment that is congruent to segment \(NM\) is segment \(KL\).