Theorem 5-8

If two lines are parallel, then all points on one line are equidistant from the other line

By Theorem 5-8, the blue lines are equidistant

Theorem 5-9

IF three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

 Segment AB is congruent to segment BC and segment DE is congruent to segment EF by theorem 5-9

Theorem 5-10

A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the mid point of the third side.

By theorem 5-10, point M is the midpoint of segment AC because the parallel line crosses segment AB at the midpoint (L)

Theorem 5-11

The segment that joins the midpoints of two sides of a triangle is (1) parallel to the third side; (2) half as long as the third side.

By theorem  5-11, segment LM is half as long as segment BC and they are both parallel.