If lm || eg, then δlfm ~ δefg by aa. one congruent pair of angles are angle flm and angle feg. how do you know those angles are congruent? triangle efg with side eg parallel to segment lm which has the point l on side ef and the point m on side fg

Answer: if i am understanding your description correctly, then the angles would be alternating interior angles, therefore they would be congruent.in the description that you gave, the angles that you listed are on opposite sides of a transversal of a pair of parallel lines. these angles are called alternate interior angles and they are always congruent.