Final answer:
To prove that AB is parallel to AC, we can use the property that if two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.
Step-by-step explanation:
Triangle ABC is a triangle with points D and F marked on side AB and points E and G marked on side AC. Segments DE and FG are drawn. If DE is parallel to FG, then line segment AB is parallel to line segment AC.
To prove this, we can use the property that if two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel. In this case, since DE is parallel to FG, the alternate interior angles formed by DE and AB as well as FG and AC are congruent. Therefore, AB is parallel to AC.