In the diagram below, line segments MR and NQ are parallel, and lines segments OR and PQ are parallel. Points N and O lie on the line segment MP.

Question

Select a phrase for each blank to make the sentence true.

Triangle NZO and triangle MRO are

because they have

.

Answer 1

Triangle NZO and triangle MRO are similar because they have equal corresponding angles.

This is true because parallel lines imply that alternate interior angles are equal, and the triangles share angle M.